Renewable bioelectronic interface for electrobiocatalytic reactor

ABSTRACT

An inexpensive, easily renewable bioelectronic device useful for bioreactors, biosensors, and biofuel cells includes an electrically conductive carbon electrode and a bioelectronic interface bonded to a surface of the electrically conductive carbon electrode, wherein the bioelectronic interface includes catalytically active material that is electrostatically bound directly or indirectly to the electrically conductive carbon electrode to facilitate easy removal upon a change in pH, thereby allowing easy regeneration of the bioelectronic interface.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation of U.S. application Ser. No.12/766,169, filed Apr. 23, 2010, entitled ELECTROBIOCATALYTIC REACTORSHAVING REVERSIBLE BIOELECTRONIC INTERFACES AND METHODS AND DEVICESRELATED THERETO, now issued as U.S. Pat. No. 9,406,959, whichapplication claimed the benefit of U.S. Provisional Application Ser. No.61/172,337, filed May 24, 2009, entitled BIOELECTRONIC INTERFACE DEVICE,each of which is hereby incorporated by reference herein in itsentirety.

FIELD OF THE INVENTION

The present invention relates to bioelectronic interfaces that promoteelectrical communication between a catalytically active material and anelectrode to facilitate chemical reactions in an electrobiocatalyticreactor, to produce electricity in a biofuel cell, or to detect ananalyte with a biosensor.

BACKGROUND OF THE INVENTION

Bioelectronic interfaces that achieve electrical communication betweenredox enzymes and an electrode have applications as biosensors(Armstrong et al., 1997, Halbhuber et al., 2003, Zayats et al., 2002),biocatalysts (Park et al., 1999, Park et al., 2003, Park and Zeikus,1999, Tsujimura et al., 2001), and biofuel cells (Chen et al., 2001,Park and Zeikus, 2003). Development of bioelectronic interfaces isespecially challenging for dehydrogenase enzymes, whose activityrequires the presence of an electron carrying cofactor [e.g.,β-nicotinamide adenine dinucleotide (phosphate) (NAD(P)⁺)] in theRossmann fold of the enzyme. The cofactor facilitates the transfer ofelectrons between the redox center of the enzyme and the electrode.However, direct electrochemical oxidation of NADH requires the use ofhigh overpotentials, which may lead to cofactor degradation (Blaedel andJenkins, 1975, Schmakel et al., 1975). Cofactor degradation can becircumvented using an electron mediator, such as toluidine blue O (TBO),Nile blue A, or neutral red to shuttle electrons between the electrodeand cofactor at moderate potentials (Molina et al., 1999, Pasco et al.,1999).

Several approaches have been used to achieve mediated electron exchange,including the development of linear (Zayats et al., 2002, Hassler etal., 2007) and branched (Hassler et al., 2007, Hassler and Worden, 2006)molecular architectures that simultaneously hold the electrode,mediator, cofactor, and enzyme in close proximity, allow unimpededaccess of the cofactor to its binding site on the enzyme, provideefficient, multistep electron transfer, and prevent component loss dueto diffusion. However, these fabrication methods involve covalentlinkages and make no provision for removal and replacement of labilecomponents, such as the enzyme and cofactor, which have limitedlifetimes. Long-term operation requires interface assembly methods thatallow periodic removal and replacement of these components.

A method to fabricate renewable bioelectronic interface on goldelectrodes (Hassler et al., 2007) has been developed. This method allowsfacile removal and replacement of the cofactor and enzyme. The approachuses layer-by-layer deposition of polyelectrolytes to reversibly bindthe cofactor and enzyme, so that they can be removed by reducing pH andthen replaced to regenerate the bioelectronic activity (Hassler et al.,2007).

However, because this method uses a thiol linkage to anchor theinterface to the gold electrode, it may not be suitable for otherelectrode materials. In addition, thiol bonds may have disadvantages forcertain applications. Alkanethiols tend to desorb at potentials outsidethe potential window defined by 800 to −1400 mV (vs Ag/AgCl) (Walczak etal., 1991, Widrig et al., 1991) and at temperatures over 100° C. (Bhatiaand Garrison, 1997). Also, the gold/thiol junction generates asignificant tunneling barrier (−2 eV) (Ranganathan et al., 2001).Alkoxy-terminated silanes can react with surface hydroxyl groups onmetal-oxide electrodes to form a polysiloxane linkage (Curran et al.,2005, Quan et al., 2004). However, Kraft has reported that metal oxidesubstrates are not stable during anodic potential cycling, due to theanodic dissolution of the metal-oxide coating (Kraft et al., 1994).

SUMMARY OF THE INVENTION

In accordance with certain aspects of the invention, there is provided abioelectronic device comprising an electrically conductive carbonelectrode and a bioelectronic interface that is bonded to a surface ofthe electrically conductive carbon electrode, wherein the interfaceincludes a catalytically active material that facilitates electrontransfer, and wherein the catalytically active material iselectrostatically bound directly or indirectly to the electricallyconductive carbon electrode, thereby facilitating easy removal andreplacement of components of the interface that may become degradedduring use.

In accordance with other aspects of the invention, a process forreconstituting a bioelectronic interface of a bioelectronic device isprovided. The process includes providing a bioelectronic device havingan electrically conductive carbon electrode and a bioelectronicinterface that includes catalytically active material, and which iselectrostatically bound directly or indirectly to a surface of theelectrically conductive carbon electrode, and thereafter exposing thebioelectronic interface to an aqueous medium having a pH that releasesthe catalytically active material from the surface of the electricallyconductive carbon electrode, then exposing the electrically conductivecarbon electrode to an aqueous medium that has a second pH thatfacilitates electrostatic bonding of a catalytically active material tothe surface of the electrically conductive carbon electrode; andintroducing fresh catalytically active material to the aqueous medium,and electrostatically bonding the fresh catalytically active material tothe surface of the electrically conductive carbon electrode, therebyrenewing the interface.

Certain aspects of the invention provide a relatively simple method bywhich the bioelectronic interface is renewed (immersing the electrodesequentially in multiple solutions, each of which contains solublereactants that are added to the interface) and may offer a majoradvantage for bioreactor operation. Specifically, the carbon electrodes(e.g., reticulated vitreous carbon) could have the old interface removedand a new one installed without removing the electrodes from thereactor. The approach would involve flowing appropriate solutionsthrough the reactor. This feature might preclude the need to remove thecarbon electrodes from the reactor, processing them, and then returningthem to the reactor each time the enzyme needs to be replaced.

In accordance with a further aspect of the invention, anelectrobiocatalytic reactor includes a cathode compartment containing afirst electrolytic solution and an anode component compartmentcontaining a second electrolytic solution, wherein the anode compartmentand the cathode compartment are separated by a proton-permeablemembrane; a cathode located at the cathode compartment and in contactwith the first electrolyte, and an anode located at the anodecompartment and in contact with the second electrolyte, wherein at leastone of the anode and cathode is an electrically conductive carbonelectrode; and a bioelectronic interface bonded to a surface of at leastone electrically conductive carbon electrode, wherein the bioelectronicinterface includes a catalytically active material that facilitateselectron transfer, and wherein the catalytically active material iselectrostatically bound directly or indirectly to the electricallyconductive carbon electrode. As is understood by those having ordinaryskill in the art, such electrobiocatalytic reactors are configurable foruse as biosensors for detecting and/or quantifying analytes, for use inconducting chemical reactions to form a desired product or degrade anundesirable compound, or for use as a biofuel cell.

The bioelectronic interface in accordance with certain aspects of theinvention is assembled layer by layer, by alternately immersing theelectrode in solutions containing polyelectrolytes having oppositecharges. Because each polyelectrolyte layer added to the interfacecontributes a thickness of about one to five nanometers, this approachprovides excellent control over the thickness of the bioelectronicinterface. Such control is not possible for other types ofimmobilization schemes. In both our experimental and modeling work, weobserved the interface developed using known techniques was either toothick or too thin and the reaction rate was low. Our approach, whichenables us to assemble the optimum, thickness by controlling how manybioelectronic cassettes we assemble, provides a facile method to achievethe optimal interface thickness.

These and other features, advantages and objects of the presentinvention will be further understood and appreciated by those skilled inthe art by reference to the following specification, claims and appendeddrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a cyclic voltammogram for the preparation of a Gly-modifiedGCE. Scan Rate 100 mV s⁻¹; supporting electrolyte: phosphate buffersolution (pH 7.4).

FIG. 1A is an electrobiocatalytic reactor.

FIG. 2 is the N(1s) region of the XPS spectrum of the (1) bare GCE, (2)GCE after soaking in 100 mM Gly for 1 h, and (3) GCE after beingelectrooxidized by cyclic voltammetry between −1.5 and 2.5 V in a 50 mMGly solution for 14 cycles.

FIGS. 3A and 3B are Nyquist plots of (A): (1) Gly, (2) Gly-TBO, (3)Gly-TBO-PEI, (4) Gly-TBO-PEI-NADH, and (5)Gly-TBO-PEI-NADH-TmMtDH-modifled electrode 100 mM PBS (pH 6.0)containing 10 mM Fe(CN)6⁻³, 10 mM Fe(CN)6⁻⁴, and 10 mM NaCl recorded at221 mV and room temperature, and (B): (1)Gly-TBO-PEI-NADH-TmMtDH-modified electrode after washing with 10 mM HCland the (2) Gly-TBO-PEI-NADH-TmMtDH-modified electrode after interfaceremoval and reconstitution.

FIGS. 4A and 4B are (A) cyclic voltammograms of theGly-TBO-PEI-NADH-functionalized electrode at various times of TmMtDH ofreconstitution: (1) 0 min, (2) 6 min, (3) 15 min, (4) 30 min, (5) 60min, (6) 120 min and (7) 240 min. (The data were recorded in 100 mM PBS(pH 6.0) containing 250 mM fructose at 60° C., and potential scan rateof 100 mV s⁻¹.), and (B) Peak electrocatalytic current at various timeintervals, respectively.

FIGS. 5A and 5B are (A) cyclic voltammograms of theGly-TBO-PEI-NADH-TmMtDH-functionalized electrode in 100 mM PBS (pH 6.0)containing 250 mM fructose at 60° C., at various potential scan rates:(1) 40 mV s⁻¹ (2) 60 mV s⁻¹, (3) 80 mV s⁻¹, (4) 100 mV s⁻¹, (5) 150 mVs⁻¹ (6) 200 mV s⁻¹, and (7) 300 mV s⁻¹, and (B) Dependence of anodic andcathodic peak currents on scan rate, respectively, with the error barsin FIG. 5B indicating the mean±the standard deviation (n=3).

FIG. 6 is a cyclic voltammograms of theGly-TBO-PEI-NADH-TmMtDH-functionalized electrode in 100 mM PBScontaining 250 mM fructose at 60° C., at various pHs: (1) 2.0, (2) 4.0,(3) 6.0, (4) 8.0, and (5) 10.0.

FIG. 7 is a plot of Log (Y″/ω) vs log (ω) plots for theGly-TBO-PEI-NADH-TmMtDH-functionalized GCE in 100 mM PBS (pH 6.0),E=−200 mV. Solid line represents the best fit of the circuit. Inset:Equivalent circuit employed in study of the impedance spectra.

FIG. 8 is a chronoamperometric current transient following a potentialstep from Einitial=100 mV to Enna=−600 mV in 100 mM PBS (pH 6.0)containing 250 mM fructose at 60° C. for the Gly-TBO-PEI-NADHTmMtDH-functionalized electrode.

FIGS. 9A and 9B are (A) cyclic voltammograms of theGly-TBO-PEI-NADH-TmMtDH-functionalized electrode in the presence ofdifferent concentrations of fructose in 100 mM PBS (pH 6.0) at 60° C.:(1) 0 mM, (2) 50 mM, (3) 100 mM, (4) 150 mM, (5) 200 mM, (6) 250 mM, (7)300 mM, and (8) 350 mM, with the data recorded at a potential scan rateof 100 mV s⁻¹, and (B) peak electrocatalytic current at various fructoseconcentrations, respectively, with the error bars in FIG. 9B indicatingthe mean±the standard deviation (n=3).

FIG. 10 is a schematic illustration of a typical enzyme membraneelectrode showing the processes considered in a mathematical model forsimulating and optimizing performance characteristics of an enzyme-basedbioelectronics interface.

FIGS. 11A and 11B are plots of product formation reaction rate versusdimensionless substrate concentration and the multiplicative reciprocalof product reaction rate versus the multiplicative reciprocal of thedimensionless substrate concentration at various product concentrations.

FIGS. 12A and 12B illustrate the effects of the ratios of the substrateand product species concentrations to the Michaelis-Menten constant forthe substrate and product, respectively.

FIGS. 13A and 13B are plots of the effectiveness factor of thebioelectronic interface as a function of the observed Thiele moduluswith respect to the substrate and product, respectively.

FIG. 14 is a plot of the effectiveness factor of the bioelectronicinterface as a function of the observed Thiele modulus for the mediator.

FIGS. 15A and 15B are dimensionless steady state voltammograms atvarious forward and reverse enzyme reaction rates, respectively.

FIG. 16 shows dimensionless steady state voltammograms that illustratethe effect of mediator kinetics on oxidation current, reduction current,and the apparent oxidation over potential of theenzyme/mediator-modified electrode.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

One aspect of the present invention is a unique bioelectronic interfacethat holds an electron mediator, cofactor, and enzyme to an electricallyconductive carbon electrode (such as a glassy carbon electrode-GCE) in amolecular orientation that allows multistep electron transfer betweenthe enzyme and electrode. Interface fabrication is based on molecularself-assembly via reversible, pH-dependent ionic interactions, allowingthe cofactor and enzyme to be removed via a change in pH, and thenreplaced to regenerate the biocatalytic activity.

Another aspect of the present invention is a biocatalytic reactorincluding one or more electrodes having bioelectronic interfacesfabricated according to the unique processes described herein. Theelectrodes may comprise a carbon substrate having a renewablebioelectronic interface.

Another aspect of the present invention is a method of designing and/oroptimizing a biocatalytic reactor or other device including abioelectronic interface. The method includes using a mathematical modelthat describes bioelectronic interfaces containing reversible enzymes,cofactors, and mediators.

As used herein, the term “bioelectronic device” refers to any devicehaving an electrode with a bioelectronic interface used to facilitate anelectrochemical reaction.

The term “bioelectronic interface” refers to an interface containing abiochemically active substance, and which is assembled on an inorganicelectrode surface to facilitate a biochemically mediated electrochemicalreaction.

The term “catalytically active material” refers to a material thatinitiates or accelerates an electrochemical reaction without itselfbeing consumed, although some degradation may occur innon-stoichiometric proportion. Catalytically active materials include,but are not necessarily limited to, enzymes.

The term “electrostatically bound” is used herein to refer to a bondformed by the attraction of oppositely charged ions.

The term “ionic moiety” refers to an atom or group of atoms that isionic or capable of being ionized.

The term “polyelectrolyte” refers to a molecule, typically a largemolecule, but not necessarily a polymer, having a plurality of ionizingmoieties.

The term “linking moiety” refers to a group of atoms bound together,which reacts with a carbon atom or some other atom on the surface of anelectrically conductive carbon electrode to form a covalent bond (e.g.,a carbon-nitrogen bond), whereby the substance containing the linkingmoiety is bound to the carbon electrode.

The term “ionic linker” refers to a molecule or substance that containsat least one linking moiety, which binds the ionic linker to aconductive carbon electrode, and at least one ionic moiety(s), whichenables other substances to be electrostatically bound to the ioniclinker.

The term, “proton permeable membrane” refers to a semi-permeablemembrane that selectively transports protons (actually hydronium ions)while being impermeable to the products and reactants of anelectrochemical reaction.

An electrobiocatalytic reactor (FIG. 1A) according to an aspect of thepresent invention includes a vessel or container 2 containing one ormore conductive electrodes 3A and 3B onto which a bioelectronicinterface is attached. The electrode(s) are preferably made of aconductive carbon material. In the illustrated example, the reactor 1includes a cathode compartment 4 and anode compartment 5 that areseparated by an optional proton permeable membrane 6. Reactor 1 may beutilized to simultaneously carry out a reduction reaction in the cathodecompartment 4 and an oxidation reaction in the anode compartment 5. Insome applications, a proton permeable membrane is not needed, and theanode and cathode are present in the same compartment.

According to one aspect of the present invention, alcohols are producedin the cathode compartment 4 from ketones or aldehydes, and ketones oraldehydes are produced in the anode compartment 5 from alcohols. Protons(H⁺) produced by the oxidation reaction at the anode pass through theproton-permeable membrane 6, and are consumed by the reduction reactionat the cathode. Electrons generated by the oxidation reaction at theanode are delivered to the cathode through an external electricalcircuit 10, and are consumed by the reduction reaction at the cathode.

According to one aspect of the present invention, bioreactor 1 (FIG. 1A)may be configured to produce mannitol from glucose in the cathodecompartment 4 using the enzymes xylose isomerase (XI) and mannitoldehydrogenase (MtDH). Simultaneously, the bioreactor 1 may producedihydroxyacetone from glycerol in the anode compartment 4 using enzymeglycerol dehydrogenase. When the bioreactor 1 is configured in this way,an aqueous glucose solution flows into the cathode compartment 4, whereit contacts a carbon electrode 3A (the cathode) that is coated with abioelectronic interface containing both MtDH and XI. Examples ofbioelectronic interfaces and methods of fabricating such interfaces aredescribed in more detail below. The XI converts the glucose to fructose,which is then converted into mannitol by the MtDH. Electrons consumed inthe second reaction are transferred from the cathode 3A to the MtDHenzyme. An electron mediator (e.g., toluidine blue O) and/or a cofactor(e.g., NADH) may be used to facilitate electron transfer between thecathode 3A and the MtDH. At the same time, an aqueous glycerol solution8 flows into the anode compartment 5, where it contacts a second carbonelectrode 3B (the anode) that is coated with a bioelectronic interfacecontaining glycerol dehydrogenase. The glycerol dehydrogenase oxidizesthe glycerol to dihydroxyacetone. Electrons produced in this reactionare transferred from the glycerol dehydrogenase to the anode 3B. Anelectron mediator (e.g. toluidine blue O) and/or a cofactor (e.g., NADH)may be used to facilitate electron transfer between the glyceroldehydrogenase and the anode 3B.

Bioreactor 1 may be configured in a variety of ways. A wide variety ofreactants and redox enzymes may be substituted to form many differentproducts. Enzymes are commonly classified using nomenclature based onEnzyme Commission (EC) number. The present invention applies to severaltypes of oxidoreductases (EC1). Numerous EC1s are listed in Table 1.Transferases, transaminases, hydrolases, lyases, isomerases, and ligasesthat may be employed in combination with the oxidoreductases are alsolisted in Table 1.

TABLE 1 EC Number Chemical Name OXIDOREDUCTASES 1.1.1.1 Alcoholdehydrogenase 1.1.1.3 Homoserine dehydrogenase 1.1.1.8Glycerol-3-phosphate dehydrogenase 1.1.1.9 D-Xylulose reductase 1.1.1.10l-Xylulose reductase 1.1.1.14 l-Iditol dehydrogenase 1.1.1.19Glucuronate reductase 1.1.1.21 Aldehyde reductase 1.1.1.22 UDPglucosedehydrogenase 1.1.1.23 Histidinol dehydrogenase 1.1.1.25 Shikimatedehydrogenase 1.1.1.27 Lactate dehydrogenase 1.1.1.29 Glyceratedehydrogenase 1.1.1.30 3-Hydroxybutyrate dehydrogenase 1.1.1.313-Hydroxyisobutyrate dehydrogenase 1.1.1.32 Mevaldate reductase 1.1.1.34Hydroxymethylglutaryl-CoA reductase (NADPH) 1.1.1.35 3-Hydroxyacyl-CoAdehydrogenase 1.1.1.37 Malate dehydrogenase 1.1.1.39 Malatedehydrogenase (decarboxylating) 1.1.1.41 Isocitrate dehydrogenase (NAD+)1.1.1.44 Phosphogluconate dehydrogenase (decarboxylating) 1.1.1.45l-Gulonate dehydrogenase 1.1.1.49 Glucose-6-phosphate dehydrogenase1.1.1.56 Ribitol dehydrogenase 1.1.1.79 Glyoxylate reductase (NADP+)1.1.1.81 Hydroxypyruvate reductase 1.1.1.82 Malate dehydrogenase (NADP+)1.1.1.85 3-Isopropylmalate dehydrogenase 1.1.1.86 Ketol-acidreductoisomerase 1.1.1.95 Phosphoglycerate dehydrogenase 1.1.1.1003-Oxoacyl-[acyl-carrier-protein] reductase 1.1.1.1023-Dehydrosphinganine reductase 1.1.1.105 Retinol dehydrogenase 1.1.1.1303-Dehydro-L-gulonate 2-dehydrogenase 1.1.1.157 3-Hydroxybutyryl-CoAdehydrogenase 1.1.1.158 UDP-N-acetylmuramate dehydrogenase 1.1.1.1692-Dehydropantoate 2-reductase 1.1.1.204 Xanthine dehydrogenase 1.1.1.205IMP-dehydrogenase 1.1.3.8 l-Gulonolactone oxidase 1.1.3.22 Xanthineoxidase 1.1.99.1 Choline dehydrogenase 1.1.99.5 Glycerol-3-phosphatedehydrogenase 1.2.1.3 Aldehyde dehydrogenase (NAD+) 1.2.1.7 Benzaldehydedehydrogenase (NADP+) 1.2.1.8 Betaine-aldehyde dehydrogenase 1.2.1.11Aspartate-semialdehyde dehydrogenase 1.2.1.12 Glyceraldehyde-3-phosphatedehydrogenase 1.2.1.13 Glyceraldehyde-3-phosphate dehydrogenase 1.2.1.16Succinate-semialdehyde dehydrogenase (NAD(P)+) 1.2.1.18 Malonatesemialdehyde dehydrogenase (acetylating) 1.2.1.21 Glycolaldehydedehydrogenase 1.2.1.23 2-Oxoaldehyde dehydrogenase (NAD+) 1.2.1.24Succinate-semialdehyde dehydrogenase 1.2.1.25 2-Oxoisovaleratedehydrogenase (acylating) 1.2.1.27 Methylmalonate-semialdehydedehydrogenase (acylating) 1.2.1.31 l-Aminoadipate-semialdehydedehydrogenase 1.2.1.32 Aminomuconate-semialdehyde dehydrogenase 1.2.1.36Retinal dehydrogenase 1.2.1.41 Glutamate-5-semialdehyde dehydrogenase1.2.1.52 Oxoglutarate dehydrogenase 1.2.3.5 Glyoxylate oxidase 1.2.3.7Indole-3-acetaldehyde oxidase 1.2.4.1 Pyruvate dehydrogenase (lipoamide)1.2.4.2 Oxoglutarate dehydrogenase (lipoamide) 1.2.7.1 Pyruvate synthase1.2.7.2 2-Oxobutyrate synthase 1.3.1.1 Dihydrouracil dehydrogenase(NAD+) 1.3.1.2 Dihydropyrimidine dehydrogenase (NADP+) 1.3.1.8 Acyl-CoAdehydrogenase (NADP+) 1.3.1.9 Enoyl-[acyl-carrier-protein] reductase(NADH) 1.3.1.10 Enoyl-[acyl-carrier-protein] reductase (NADPH,B-specific) 1.3.1.13 Prephenate dehydrogenase (NADP+) 1.3.1.14 Orotatereductase (NADH) 1.3.1.26 Dihydrodipicolinate reductase 1.3.1.35Phosphatidylcholine desaturase 1.3.3.3 Coproporphyrinogen oxidase1.3.3.4 Protoporphyrinogen oxidase 1.3.5.1 Succinate dehydrogenase(ubiquinone) 1.3.99.1 Succinate dehydrogenase 1.3.99.2 Butyryl-CoAdehydrogenase 1.3.99.3 Acyl-CoA dehydrogenase 1.3.99.7 Glutaryl-CoAdehydrogenase 1.3.99.10 Isovaleryl-CoA dehydrogenase 1.4.1.1 Alaninedehydrogenase 1.4.1.2 Glutamate dehydrogenase 1.4.1.7 Serinedehydrogenase 1.4.1.8 Valine dehydrogenase (NADP+) 1.4.1.9 Leucinedehydrogenase 1.4.1.10 Glycine dehydrogenase 1.4.1.14 Glutamate synthase(NADH) 1.4.1.19 Tryptophan dehydrogenase 1.4.3.1 d-Aspartate oxidase1.4.3.2 l-Amino-acid oxidase 1.4.3.4 Amine oxidase (flavin-containing)1.4.3.8 Ethanolamine oxidase 1.4.4.2 Glycine dehydrogenase(decarboxylating) 1.5.1.2 Pyrroline-5-carboxylate reductase 1.5.1.3Dihydrofolate reductase 1.5.1.5 Methylenetetrahydrofolate reductase(NADP+) 1.5.1.6 Formyltetrahydrofolate dehydrogenase 1.5.1.7Saccharopine dehydrogenase (NAD+, L-lysine-forming) 1.5.1.8 Saccharopinedehydrogenase (NADP+, L-lysine-forming) 1.5.1.9 Saccharopinedehydrogenase (NAD+, L-glutamate-forming) 1.5.1.10 Saccharopinedehydrogenase (NADP+, L-glutamate- forming) 1.5.1.121-Pyrroline-5-carboxylate dehydrogenase 1.5.3.1 Sarcosine oxidase1.5.99.1 Sarcosine dehydrogenase 1.5.99.2 Dimethylglycine dehydrogenase1.5.99.8 Proline dehydrogenase 1.6.4.1 Cystine reductase (NADH) 1.6.5.3NADH dehydrogenase (ubiquinone) 1.6.6.1 Nitrate reductase (NADH) 1.6.6.2Nitrate reductase [NAD(P)H] 1.6.6.3 Nitrate reductase (NADPH) 1.6.6.4Nitrite reductase [NAD(P)H] 1.6.6.8 GMP reductase 1.7.3.3 Urate oxidase1.7.7.1 Ferredoxin-nitrate reductase 1.7.99.4 Nitrate reductase 1.8.1.3Hypotaurine dehydrogenase 1.8.1.4 Dihydrolipoamide dehydrogenase 1.8.2.1Sulfite dehydrogenase 1.8.3.1 Sulfite oxidase 1.8.7.1 Sulfite reductase(ferredoxin) 1.8.99.1 Sulfite reductase 1.8.99.2 Adenylsulphatereductase 1.9.3.1 Cytochrome-c oxidase 1.10.2.1l-Ascorbate-cytochrome-b5 reductase 1.10.2.2 Ubiquinol-cytochrome-creductase 1.10.3.3 l-Ascorbate oxidase 1.10.99.1Plastoquinol-plastocyanin reductase 1.13.11.1 Catechol 1,2-dioxygenase1.13.11.2 Catechol 2,3-dioxygenase 1.13.11.5 Homogentisate1,2-dioxygenase 1.13.11.6 3-Hydroxyanthranilate 3,4-dioxygenase1.13.11.11 Tryptophan 2,3-dioxygenase 1.13.11.20 Cysteine dioxygenase1.13.11.21 β-Carotene 15,154-dioxygenase 1.13.11.274-Hydroxyphenylpyruvate dioxygenase 1.13.11.34 Arachidonate5-lipoxygenase 1.13.99.1 myo-lnositol oxygenase 1.14.11.1g-Butyrobetaine dioxygenase 1.14.11.2 Procollagen-proline dioxygenase1.14.11.8 Trimethyllysine dioxygenase 1.14.12.1 Anthranilate1,2-dioxygenase (deaminating, decarboxylating) 1.14.13.5Imidazoleacetate 4-monooxygenase 1.14.13.9 Kynurenine 3-monooxygenase1.14.13.11 trans-Cinnamate 4-monooxygenase 1.14.13.12 Benzoate4-monooxygenase 1.14.13.39 Nitric oxide synthase 1.14.16.1 Phenylalanine4-monooxygenase 1.14.16.2 Tyrosine 3-monooxygenase 1.14.16.4 Tryptophan5-monooxygenase 1.14.17.1 Dopamine β-monooxygenase 1.14.18.1 Monophenolmonooxygenase 1 14.99.1 Prostaglandin synthase 1 14.99.5 Stearoyl-CoAdesaturase 1.14.99.7 Squalene monooxygenase 1.14.99.25 Linoleoyl-CoAdesaturase 1.17.4.1 Ribonucleoside-diphosphate reductase 1.18.6.1Nitrogenase TRANSFERASES 2.1.1.1 Nicotinamide N-methyltransferase2.1.1.2 Guanidinoacetate N-methyltransferase 2.1.1.3 Thetin-homocysteineS-methyltransferase 2.1.1.4 Acetylserotonin N-methyltransferase 2.1.1.5Betaine-homocysteine S-methyltransferase 2.1.1.6 Catechol O-methyltransferase 2.1.1.10 Homocysteine S-methyltransferase 2.1.1.135-Methyltetrahydrofolate-homocysteine S-methyl transferase 2.1.1.145-Methyltetrahydropteroyltriglutamate homocysteine S-methyltransferase2.1.1.17 Phosphatidylethanolamine N-methyltransferase 2.1.1.20 GlycineN-methyltransferase 2.1.1.28 Phenylethanolamine N-methyltransferase2.1.1.45 Thymidylate synthase 2.1.1.71 Phosphatidyl-N-methylethanolamineN-methyltransferase 2.1.2.1 Glycine hydroxymethyltransferase 2.1.2.2Phosphoribosylglycinamide formyltransferase 2.1.2.3Phosphoribosylaminoimidazole carboxamide formyltransferase 2.1.2.5Glutamate formiminotransferase 2.1.2.10 Aminomethyl transferase 2.1.3.1Methylmalonyl-CoA carboxyltransferase 2.1.3.2 Aspartatecarbamoyltransferase 2.1.3.3 Ornithine carbamoyltransferase 2.1.4.1Glycine amidinotransferase 2.2.1.1 Transketolase 2.2.1.2 Transaldolase2.3.1.1 Amino-acid N-acetyltransferase 2.3.1.4 Glucosamine-phosphateN-acetyltransferase 2.3.1.5 Arylamine N-acetyltransferase 2.3.1.6Choline O-acetyltransferase 2.3.1.7 Carnitine O-acetyltransferase2.3.1.8 Phosphate acetyltransferase 2.3.1.9 Acetyl-CoAC-acetyltransferase 2.3.1.12 Dihydrolipoamide S-acetyltransferase2.3.1.15 Glycerol-3-phosphate O-acyltransferase 2.3.1.16 Acetyl-CoAC-acyltransferase 2.3.1.20 Diacylglycerol O-acyltransferase 2.3.1.23Lysolecithin acyltransferase 2.3.1.24 Sphingosine N-acyltransferase2.3.1.30 Serine O-acetyltransferase 2.3.1.37 5-Aminolevulinate synthase2.3.1.38 [Acyl-carrier-protein] S-acetyltransferase 2.3.1.39[Acyl-carrier-protein] S-malonytransferase 2.3.1.413-Oxoacyl-[acyl-carrier-protein] synthase 2.3.1.46 HomoserineO-succinyltransferase 2.3.1.50 Serine C-palmitoyltransferase 2.3.1.511-Acylglycerol-3-phosphate O-acyltransferase 2.3.1.76 RetinolO-fatty-acyltransferase 2.4.1.1 Phosphorylase 2.4.1.9 Inulosucrase 24.1.11 Glycogen (starch) synthase 2.4.1.13 Sucrose synthase 2.4.1.16Chitin synthase 2.4.1.17 Glucuranosyltransferase 2.4.1.21 Starchsynthase 2.4.1.22 Lactose synthase 2.4.1.23 Sphingosineβ-galactosyltransferase 2.4.1.29 Cellulose synthase (GDP-forming)2.4.1.32 Glucomannan 4-β-mannosyltransferase 2.4.1.33 Alginate synthase2.4.1.47 Acylsphingosine galactosyltransferase 2.4.1.62 Gangliosidegalactosyltransferase 2.4.1.68 Glycoprotein 6-a-L-fucosyltransferase2.4.1.69 Galactoside 2-a-L-fucosyltransferase 2.4.2.1 Purine-nucleosidephosphorylase 2.4.2.2 Pyrimidine-nucleoside phosphorylase 2.4.2.4Thymidine phosphorylase 2.4.2.8 Hypoxanthine phosphoribosyltransferase2.4.2.9 Uracil phosphoribosyltransferase 2.4.2.10 Orotatephosphoribosyltransferase 2.4.2.11 Nicotinate phosphoribosyltransferase2.4.2.14 Amidophosphoribosyltransferase 2.4.2.15 Guanosine phosphorylase2.4.2.17 ATP phosphoribosyltransferase 2.4.2.18 Anthranilatephosphoribosyltransferase 2.4.2.19 Nicotinate-nucleotidepyrophosphorylase (carboxylating) 2.4.99.1-11 Sialyltransferases2.4.99.7 Sialyltransferase 2.5.1.1 Dimethylallyltranstransferase 2.5.1.6Methionine adenosyltransferase 2.5.1.10 Geranyltranstransferase 2.5.1.16Spermidine synthase 2.5.1.19 3-Phosphoshikimate1-carboxyvinyl-transferase 2.5.1.21 Farnesyltransferase 2.5.1.22Spermine synthase 2.5.1.29 Farnesyltranstransferase 2.5.1.32Geranylgeranyl-diphosphate geranylgeranyl transferase TRANSAMINASES2.6.1.1 Aspartate transaminase 2.6 1.2 Alanine transaminase 2.6.1.4Glycine transaminase 2.6 1.5 Tyrosine transaminase 2.6 1.6 Leucinetransaminase 2.6.1.9 Histidinol-phosphate transaminase 2.6.1.13Ornithine-oxo-acid transaminase 2.6.1.16 Glutamine-fructose-6-phosphatetransaminase 2.6.1.17 Succinyldiaminopimelate transaminase 2.6.1.18β-Alanine-pyruvate transaminase 2.6.1.19 4-Aminobutyrate transaminase2.6.1.22 l-3-Aminoisobutyrate transaminase 2.6.1.23 4-Hydroxyglutamatetransaminase 2.6.1.27 Tryptophan transaminase 2.6.1.32Valine-3-methyl-2-oxovalerate transaminase 2.6.1.36 l-Lysine6-transaminase 2.6.1.39 2-Aminoadipate transaminase 2.6.1.42Branched-chain-amino-acid transaminase 2.6.1.44 Alanine-glyoxylatetransaminase 2.6.1.51 Serine-pyruvate transaminase 2.6.1.52Phosphoserine transaminase 2.6.1.66 Valine-pyruvate transaminase 2.7.1.1Hexokinase 2.7.1.2 Glucokinase 2.7.1.3 Ketohexokinase 2.7.1.4Fructokinase 2.7.1.6 Galactokinase 2.7.1.7 Mannokinase 2.7.1.116-Phosphofructokinase 2.7.1.15 Ribokinase 2.7.1.16 Ribulokinase 2.7.1.17Xylulokinase 2.7.1.19 Phosphoribulokinase 2.7.1.24 Dephospho-CoA kinase2.7.1.25 Adenylylsulfate kinase 2.7.1.28 Triokinase 2.7.1.30 Glycerolkinase 2.7.1.31 Glycerate kinase 2.7.1.32 Choline kinase 2.7.1.33Pantothenate kinase 2.7.1.34 Pantetheine kinase 2.7.1.36 Mevalonatekinase 2.7.1.39 Homoserine kinase 2.7.1.40 Pyruvate kinase 2.7 1.47D-Ribulokinase 2.7.1.53 l-Xylulokinase 2.7.1.60 N-Acylmannosamine kinase2.7.1.71 Shikimate kinase 2.7.1.80 Pyrophosphate-serinephosphotransferase 2.7.1.82 Ethanolamine kinase 2.7.1.107 Diacylglycerolkinase 2.7.2.3 Phosphoglycerate kinase 2.7.2.4 Aspartate kinase 2.7.2.6Formate kinase 2.7.2.11 Glutamate 5-kinase 2.7.3.2 Creatine kinase2.7.4.2 Phosphomevalonate kinase 2.7.4.3 Adenylate kinase 2.7.4.4Nucleoside-phosphate kinase 2.7.4.6 Nucleoside-diphosphate kinase2.7.4.8 Guanylate kinase 2.7.4.9 dtmp kinase 2.7.4.14 Cytidylate kinase2.7.6.1 Ribose-phosphate pyrophosphokinase 2.7.7.3 Pantetheine-phosphateadenylyltransferase 2.7.7.4 Sulfate adenylyl transferase 2.7.7.6 RNAnucleotidyltransferase (DNA-directed) 2.7.7.7 DNA nucleotidyltransferase(DNA-directed) 2.7.7.9 UTP-glucose-1-phosphate uridylyltransferase2.7.7.10 UTP-hexose-1-phosphate uridylyltransferase 2.7.7.12 UDPglucose-hexose-1-phosphate uridylyltransferase 2.7.7.13Mannose-1-phosphate guanylyltransferase 2.7.7.14 Ethanolamine-phosphatecytidylyltransferase 2.7.7.15 Choline-phosphate cytidylyltransferase2.7.7.18 Nicotinate-nucleotide adenylyltransferase 2.7.7.23UDP-N-acetylglucosamine pyrophosphorylase 2.7.7.24 Glucose-1-phosphatethymidylyltransferase 2.7.7.27 Glucose-1-phosphate adenylyltransferase2.7.7.34 Glucose-1-phosphate guanylyltransferase 2.7.7.41 Phosphatidatecytidylyltransferase 2.7.7.43 N-Acylneuraminate cytidylyltransferase2.7.8.1 Ethanolamine phosphotransferase 2.7.8.2 Diacylglycerolcholinephosphotransferase 2.7.8.3 Ceramide cholinephosphotransferase2.7.8.5 CDPdiacylglycerol-glycerol-3-phosphate 3-phosphatidyltransferase2.7.8.8 CDPdiacylglycerol-serine O-phosphatidyltransferase 2.7.8.11CDPdiacylglycerol-inositol 3-phosphatidyltransferase 2.8.3.5 3-OxoacidCoA-transferase 2.8.3.6 3-Oxoadipate CoA-transferase HYDROLASES 3.1.1.3Triacylglycerol lipase 3.1.1.4 Phospholipase A2 3.1.1.5Lysophospholipase 3.1.1.7 Acetylcholinesterase 3.1.1.17 Gluconolactonase3.1.1.21 Retinyl-palmitate esterase 3.1.1.28 Acylcarnitine hydrolase3.1.1.31 6-Phosphogluconolactonase 3.1.1.32 Phospholipase A1 3.1.2.1Acetyl-CoA hydrolase 3.1.2.3 Succinyl-CoA hydrolase 3.1.2.43-Hydroxyisobutyryl-CoA hydrolase 3.1.2.11 Acetoacetyl-CoA hydrolase3.1.2.20 Acyl-CoA hydrolase 3.1.3.2 Acid phosphatase 3.1.3.3Phosphoserine phosphatase 3.1.3.4 Phosphatidate phosphatase 3.1.3.554-Nucleotidase 3.1.3.9 Glucose-6-phosphatase 3.1.3.11Fructose-bisphosphatase 3.1.3.15 Histidinol-phosphatase 3.1.3.25myo-Inositol-1(or 4)-monophosphatase 3.1.3.27Phosphatidylglycerophosphatase 3.1.3.29 N-Acylneuraminate-9-phosphatase3.1.3.31 Nucleotidase 3.1.4.2 Glycerophosphocholine phosphodiesterase3.1.4.3 Phospholipase C 3.1.4.4 Phospholipase D 3.1.4.101-Phosphatidylinositol phosphodieterase 3.1.4.12 Sphingomyelinphosphodiesterase 3.2.1.21 β-Glucosidase 3.2.1.23 β-Galactosidase3.2.1.26 β-Fructofuranosidase 3.2.1.45 Glucosylceramidase 3.2.1.46Galactosylceramidase 3.2.1.48 Sucrose a-glucosidase 3.2.2.2 Inosinenucleosidase 3.3.1.1 Adenosylhomocysteinase 3.5.1.1 Asparaginase 3.5.1.2Glutaminase 3.5.1.6 β-Ureidopropionase 3.5.1.9 Arylformamidase 3.5.1.18Succinyl-diaminopimelate desuccinylase 3.5.1.22 Pantothenase 3.5.1.23Ceramidase 3.5.2.2 Dihydropyrimidinase 3.5.2.3 Dihydroorotase 3.5.2.5Allantoinase 3.5.2.7 Imidazolonepropionase 3.5.2.10 Creatininase 3.5.3.1Arginase 3.5.3.4 Allantoicase 3.5.3.6 Arginine deiminase 3.5.4.1Cytosine deaminase 3.5.4.3 Guanine deaminase 3.5.4.6 AMP deaminase3.5.4.10 IMP cyclohydrolase 3.5.4.12 dCMP deaminase 3.5.4.19Phosphoribosyl-AMP cyclohydrolase 3.6.1.3 Adenosinetriphosphatase3.6.1.15 Nucleoside-triphosphatase 3.6.1.31 Phosphoribosyl-ATPpyrophosphatase 3.6.1.34 H+-transporting ATP synthase 3.7.1.2Fumarylacetoacetase 3.7.1.3 Kynureninase 3.9.1.1 Phosphoamidase LYASES4.1.1.1 Pyruvate decarboxylase 4.1.1.3 Oxaloacetate decarboxylase4.1.1.4 Acetoacetate decarboxylase 4.1.1.9 Malonyl-CoA decarboxylase4.1.1.11 Aspartate 1-decarboxylase 4.1.1.12 Aspartate 4-decarboxylase4.1.1.15 Glutamate decarboxylase 4.1.1.17 Ornithine decarboxylase4.1.1.20 Diaminopimelate decarboxylase 4 1.1.21Phosphoribosylaminoimidazole carboxylase 4.1.1.22 Histidinedecarboxylase 4.1.1.23 Orotidine-5′-phosphate decarboxylase 4.1.1.25Tyrosine decarboxylase 4.1.1.28 Aromatic-L-amino-acid decarboxylase4.1.1.29 Sulfoalanine decarboxylase 4.1.1.32 Phosphoenolpyruvatecarboxykinase (GTP) 4.1.1.33 Diphosphomevalonate decarboxylase 4.1.1.34Dehydro-l-gulonate decarboxylase 4.1.1.36 Phosphopantothenoylcysteinedecarboxylase 4.1.1.37 Uroporphyrinogen decarboxylase 4.1.1.39Ribulose-bisphosphate carboxylase 4.1.1.41 Methylmalonyl-CoAdecarboxylase 4.1.1.43 Phenylpyruvate decarboxylase 4.1.1.45Aminocarboxymuconate-semialdehyde decarboxylase 4.1.1.48Indole-3-glycerol-phosphate synthase 4.1.1.49 Phosphoenolpyruvatecarboxykinase (ATP) 4.1.1.50 Adenosylmethionine decarboxylase 4.1.1.65Phosphatidylserine decarboxylase 4.1.1.71 2-Oxoglutarate decarboxylase4.1.2.5 Threonine aldolase 4.1.2.12 Ketopantoaldolase 4.1.2.13Fructose-bisphosphate aldolase 4.1.2.142-Dehydro-3-deoxyphosphogluconate aldolase 4.1.3.1 Isocitrate lyase4.1.3.2 Malate synthase 4.1.3.4 Hydroxymethylglutaryl-CoA lyase 4.1.3.5Hydroxymethylglutaryl-CoA synthase 4.1.3.7 Citrate (si)-synthase 4.1.3.8ATP citrate (pro-S)-lyase 4.1.3.16 4-Hydroxy-2-oxoglutarate aldolase4.1.3.18 Acetolactate synthase 4.1.3.20 N-Acylneuraminate-9-phosphatesynthase 4.1.3.21 Homocitrate synthase 4.1.3.22 Citramalate lyase4.1.3.27 Anthranilate synthase 4.1.99.1 Tryptophanase 4.2.1.2 Fumaratehydratase 4.2.1.3 Aconitate hydratase 4.2.1.4 Citrate dehydratase4.2.1.9 Dihydroxy-acid dehydratase 4.2.1.10 3-Dehydroxyquinatedehydratase 4.2.1.11 Phosphopyruvate hydratase (enolase) 4.2.1.13l-Serine dehydratase 4.2.1.16 Threonine dehydratase 4.2.1.17 Enoyl-CoAhydratase 4.2.1.18 Methylglutaconyl-CoA hydratase 4.2.1.19Imidazoleglycerol-phosphate dehydratase 4.2.1.20 Tryptophan synthase4.2.1.22 Cystathionine B-synthase 4.2.1.24 Porphobilinogen synthase4.2.1.33 3-Isopropylmalate dehydratase 4.2 1.46 dTDPglucose4,6-dehydratase 4.2.1.47 GDPmannose 4,6-dehydratase 4.2.1.49 Urocanatehydratase 4.2.1.51 Prephenate dehydratase 4.2.1.52 Dihydrodipicolinatesynthase 4.2.1.55 3-Hydroxybutyryl-CoA dehydratase 4.2.1.58Crotonoyl-[acyl-carrier-protein] hydratase 4.2.1.593-Hydroxyoctanoyl-[acyl-carrier protein] dehydratase 4.2.1.603-Hydroxydecanoyl-[acyl-carrier protein] dehydratase 4.2.1.613-Hydroxypalmitoyl-[acyl-carrier protein]dehydratase 4.2.1.75Uroporphyrinogen-III synthase 4.2.1.80 2-Oxopent-4-enoate hydratase4.2.99.2 Threonine synthase 4.2.99.8 Cysteine synthase 4.2.99.9O-Succinylhomoserine (thiol)-lyase 4.3.1.1 Aspartate ammonia-lyase4.3.1.2 Methylaspartate ammonia-lyase 4.3.1.3 Histidine ammonia-lyase4.3.1.5 Phenylalanine ammonia-lyase 4.3.2.1 Argininosuccinate lyase4.3.2.2 Adenylosuccinate lyase 4.4.1.1 Cystathionine g-lyase 4.4.1.8Cystathionine β-lyase 4.4.1.15 D-Cysteine desulfhydrase 4.6.1.1Adenylate cyclase 4.6.1.3 3-Dehydroquinate synthase 4.6.1.4 Chorismatesynthase 4.99.1.1 Ferrochelatase ISOMERASES 5.1.3.1 Ribulose-phosphate3-epimerase 5.1.3.2 UDPglucose 4-epimerase 5.1.3.4 l-Ribulose-phosphate4-epimerase 5.1.3.6 UDPglucuronate 4-epimerase 5.1.3.7UDP-N-acetylglucosamine 4-epimerase 5.1.3.12 UDPglucuronate 54-epimerase5.1.3.13 dTDP-4-Dehydrorhamnose 3,5-epimerase 5.1.3.14UDP-N-acetylglucosamine 2-epimerase 5.1.99.1 Methylmalonyl-CoA epimerase5.2.1.2 Maleylacetoacetate isomerase 5.2.1.3 Retinal isomerase 5.2.1.7Retinol isomerase 5.3.1.1 Triose-phosphate isomerase 5.3.1.3 Arabinoseisomerase 5.3.1.4 l-Arabinose isomerase 5.3.1.5 Xylose isomerase 5.3.1.6Ribose-5-phosphate isomerase 5.3.1.8 Mannose-6-phosphate isomerase5.3.1.9 Glucose-6-phosphate isomerase 5.3.1.16N-(54-Phospho-d-ribosylformimino)-5-amino-1-(544-phosphoribosyl)-4-imidazolecarboxamide isomerase 5.3.3.2Isopentenyl-diphosphate 3-isomerase 5.3.99.3 Prostaglandin-E synthase5.3.99.5 Thromboxane-A synthase 5.4.2.1 Phosphoglycerate mutase 5.4.2.2Phosphoglucomutase 5.4.2.3 Phosphoacetylglucosamine mutase 5.4.2.8Phosphomannomutase 5.4.3.8 Glutamate-1-semialdehyde 2,1-aminomutase5.4.99.2 Methylmalonyl-CoA mutase 5.4.99.5 Chorismate mutase 5.4.99.7Lanosterol synthase 5.5.1.4 myo-Inositol-l-phosphate synthase LIGASES6.2.1.3 Long-chain-fatty-acid-CoA ligase 6.3.1.1 Aspartate-ammonialigase 6.3.1.2 Glutamate-ammonia ligase 6.3.1.4 Aspartate-ammonia ligase(ADP-forming) 6.3.1.5 NAD+ synthetase 6.3.2.1 Pantoate-β-alannine ligase6.3.2.2 Glutamate-cysteine ligase 6.3.2.3 Glutathione synthase 6.3.2.5Phosphopantothenate-cysteine ligase 6.3.2.6Phosphoribosylaminoimidazole-succinocarboxamide synthase 6.3.2.7UDP-N-Acetylmuramoyl-l-alanyl-d-glutamate-lysine ligase 6.3.2.8UDP-N-acetylmuramate-alanine ligase 6.3.2.9UDP-N-acetylmuramoylalanine-D-glutamate ligase 6.3.2.10UDP-N-acetylmuramoylalanyl-D-glutamyl-lysine-D- alanyl-D-alanine ligase6.3.2.13 UDP-N-acetylmuramoylalanyl-D-glutamate-2,6- diaminopimelateligase 6.3.3.1 Phosphoribosylglycinamidine cyclo-ligase 6.3.4.1 GMPsynthase 6.3.4.2 CTP synthase 6.3.4.3 Formate-tetrahydrofolate ligase6.3.4.4 Adenylosuccinate synthase 6.3.4.5 Argininosuccinate synthase6.3.4.7 Ribose-5-phosphate-ammonia ligase 6.3.4.13Phosphoribosylamine-glycine ligase 6.3.4.16 Carbamoyl-phosphate synthase(ammonia) 6.3.4.17 Formate-dihydrofolate ligase 6.3.5.1 NAD+ synthetase(glutamine-hydrolysing) 6.3.5.2 GMP synthetase (glutamine-hydrolysing)6.3.5.3 Phosphoribosylformylglycinamidine synthetase 6.3.5.4 Asparaginesynthase (glutamine-hydrolysing) 6.3.5.5 Carbamoyl-phosphate synthase(glutamine-hydrolysing) 6.4.1.1 Pyruvate carboxylase 6.4.1.2 Acetyl-CoAcarboxylase 6.4.1.3 Propionyl-CoA carboxylase 6.4.1.4Methylcrotonoyl-CoA carboxylase DEHYDROGENASES 1.1.1.1 Alcoholdehydrogenase 1.1.1.3 Homoserine dehydrogenase 1.1.1.8Glycerol-3-phosphate dehydrogenase 1.1.1.14 l-Iditol dehydrogenase1.1.1.22 UDPglucose dehydrogenase 1.1.1.23 Histidinol dehydrogenase1.1.1.25 Shikimate dehydrogenase 1.1.1.27 Lactate dehydrogenase 1.1.1.29Glycerate dehydrogenase 1.1.1.30 3-Hydroxybutyrate dehydrogenase1.1.1.31 3-Hydroxyisobutyrate dehydrogenase 1.1.1.35 3-Hydroxyacyl-CoAdehydrogenase 1.1.1.37 Malate dehydrogenase 1.1.1.39 Malatedehydrogenase (decarboxylating) 1.1.1.41 Isocitrate dehydrogenase (NAD+)1.1.1.44 Phosphogluconate dehydrogenase (decarboxylating) 1.1.1.45l-Gulonate dehydrogenase 1.1.1.49 Glucose-6-phosphate dehydrogenase1.1.1.56 Ribitol dehydrogenase 1.1.1.79 Glyoxylate reductase (NADP+)1.1.1.82 Malate dehydrogenase (NADP+) 1.1.1.85 3-Isopropylmalatedehydrogenase 1.1.1.95 Phosphoglycerate dehydrogenase 1.1.1.105 Retinoldehydrogenase 1.1.1.130 3-Dehydro-L-gulonate 2-dehydrogenase 1.1.1.1573-Hydroxybutyryl-CoA dehydrogenase 1.1.1.158 UDP-N-acetylmuramatedehydrogenase 1.1.1.204 Xanthine dehydrogenase 1.1.1.205IMP-dehydrogenase 1.1.99.1 Choline dehydrogenase 1.1.99.5Glycerol-3-phosphate dehydrogenase 1.2.1.3 Aldehyde dehydrogenase (NAD+)1.2.1.7 Benzaldehyde dehydrogenase (NADP+) 1.2.1.8 Betaine-aldehydedehydrogenase 1.2.1.11 Aspartate-semialdehyde dehydrogenase 1.2.1.12Glyceraldehyde-3-phosphate dehydrogenase 1.2.1.13Glyceraldehyde-3-phosphate dehydrogenase 1.2.1.16 Succinate-semialdehydedehydrogenase (NAD(P)+) 1.2.1.18 Malonate semialdehyde dehydrogenase(acetylating) 1.2.1.21 Glycolaldehyde dehydrogenase 1.2.1.232-Oxoaldehyde dehydrogenase (NAD+) 1.2.1.24 Succinate-semialdehydedehydrogenase 1.2.1.25 2-Oxoisovalerate dehydrogenase (acylating)1.2.1.27 Methylmalonate-semialdehyde dehydrogenase (acylating) 1.2.1.31l-Aminoadipate-semialdehyde dehydrogenase 1.2.1.32Aminomuconate-semialdehyde dehydrogenase 1.2.1.36 Retinal dehydrogenase1.2.1.41 Glutamate-5-semialdehyde dehydrogenase 1.2.1.52 Oxoglutaratedehydrogenase 1.2.4.1 Pyruvate dehydrogenase (lipoamide) 1.2.4.2Oxoglutarate dehydrogenase (lipoamide) 1.3.1.1 Dihydrouracildehydrogenase (NAD+) 1.3.1.2 Dihydropyrimidine dehydrogenase (NADP+)1.3.1.8 Acyl-CoA dehydrogenase (NADP+) 1.3.1.13 Prephenate dehydrogenase(NADP+) 1.3.5.1 Succinate dehydrogenase (ubiquinone) 1.3.99.1 Succinatedehydrogenase 1.3.99.2 Butyryl-CoA dehydrogenase 1.3.99.3 Acyl-CoAdehydrogenase 1.3.99.7 Glutaryl-CoA dehydrogenase 1.3.99.10Isovaleryl-CoA dehydrogenase 1.4.1.1 Alanine dehydrogenase 1.4.1.2Glutamate dehydrogenase 1.4.1.7 Serine dehydrogenase 1.4.1.8 Valinedehydrogenase (NADP+) 1.4.1.9 Leucine dehydrogenase 1.4.1.10 Glycinedehydrogenase 1.4.1.19 Tryptophan dehydrogenase 1.4.4.2 Glycinedehydrogenase (decarboxylating) 1.5.1.6 Formyltetrahydrofolatedehydrogenase 1.5.1.7 Saccharopine dehydrogenase (NAD+,L-lysine-forming) 1.5.1.8 Saccharopine dehydrogenase (NADP+,L-lysine-forming) 1.5.1.9 Saccharopine dehydrogenase (NAD+,L-glutamate-forming) 1.5.1.10 Saccharopine dehydrogenase (NADP+,L-glutamate- forming) 1.5.1.12 1-Pyrroline-5-carboxylate dehydrogenase1.5.99.1 Sarcosine dehydrogenase 1.5.99.2 Dimethylglycine dehydrogenase1.5.99.8 Proline dehydrogenase1 1.6.5.3 NADH dehydrogenase (ubiquinone)1.8.1.3 Hypotaurine dehydrogenase 1.8.1.4 Dihydrolipoamide dehydrogenase1.8.2.1 Sulfite dehydrogenase

The approach described in more detail below could be applied to varioussubclasses of oxidoreductase enzymes. For example, the interface usedfor oxidoreductases acting on NADH could readily be adapted tooxidoreductases acting on flavodoxin as donor by substituting FADH₂ forNADH when assembling the interface.

In certain embodiments of the invention, the bioelectronic interface isfabricated on a glassy carbon electrode (GCE) using a carbon-nitrogenbond, which is stable at both high potentials (−1100 mV to 1100 mV) andhigh temperatures (Adams, 1969, Woodward, 1985). However, otherelectrically conductive carbon electrodes may be used, includingvitreous reticulated carbon electrodes.

One aspect of the present invention is a method comprising molecularself assembly that is utilized to fabricate renewable bioelectronicinterfaces on GCEs. Glycine (Gly) and the polycation poly(ethyleneimine)(PEI) may be used to couple the electron mediator, cofactor, and enzymeto a GCE in such a way that mediated electron transfer is achieved. Theenzyme and cofactor may be removed by either raising or lowering the pHof the solution. Lowering the pH would protonate surface-boundcarboxylic acid groups and thereby disrupt the electrostaticinteractions between these groups and positively charged amine groups onthe cofactor- and enzyme-modified PEI. After returning the pH to a valueabove the acid group's pK, PEI containing fresh cofactor and enzyme maythen be reattached to regenerate bioelectronic activity. Raising the pHwould deprotonate the positively charged amine groups on the cofactor-and enzyme-modified PEI and thereby disrupt the electrostaticinteractions between these groups and surface-bound carboxylic acidgroups. After returning the pH to a value below the amine group's pK,PEI containing fresh cofactor and enzyme may then be reattached toregenerate bioelectronic activity. Atomic force microscopy (AFM),chronoamperometry, constant potential amperometry, cyclic voltammetry,electrochemical impedance spectroscopy (EIS), and X-ray photoelectronspectroscopy (XPS) have been utilized to demonstrate the assemblyprocess and the electrical activity of the resulting bioelectronicinterface.

As another alternative, the carbon electrode may be treated, such aswith a plasma, to ionize the surface and allow electrostatic bonding ofa polyelectrolyte linker directly to the treated surface of theelectrode.

Materials and Methods

Media and Strains

Mannitol dehydrogenase from Thermotoga maritima (TmMtDH) was expressedin E. coli BL21(DE3) (TmMtDH) and purified as previously described (Songet al., 2008).

Chemicals

Glycine (Gly), n-hydroxysuccinimide (NHS),1-ethyl-3-(3-dimethylaminopropyl) carbodiimide (EDC), toluidine blue O(TBO), 3-carboxyphenyl boronic acid (CBA), β-nicotinamide adeninedinucleotide (NADH), PEI, glutaric dialdehyde (25% in water),D-fructose, D-glucose, sorbose, and arbinose were purchased fromSigma-Aldrich (St. Louis, Mo.). Ultrapure water (18.2 MΩ) was suppliedby a Barnstead Nanopure-UV four-stage purifier (Barnstead International,Dubuque, Iowa).

Interface Formation

The GCEs (3 mm diameter, CH Instruments, Austin, Tex.) were polished onmicrocloth pads using 0.05 μm alumina powder (CH Instruments) and rinsedthoroughly with distilled water in an ultrasonic bath for 10 minutes.The cleaned electrodes were treated in a 100 mM phosphate buffersolution (PBS) (pH 7.4) containing 100 mM Gly by 14 cycles of cyclicvoltammetry between 2500 mV and −1500 mV at a scan rate (ν) of 100 mVs⁻¹ and then washed with ethanol and double distilled water to removephysically adsorbed material. After immobilization, the electrodes werewashed with ethanol and water to remove the remaining unbound Gly. Afterdrying in air, a blue thin film could be seen at the electrode surface.The thickness of the film could be controlled by the number of scans andthe concentration of Gly.

The GCEs were incubated for 1 h in 0.1 mM TBO in 100 mM PBS (pH 7.4) inthe presence of 2 mM NHS and 2 mM EDC, resulting in formation of anamide linkage between the amine group of the TBO and the carboxylic acidgroup of the Gly (Gly-TBO). The Gly-TBO-modified electrodes were soakedin a 10 mM aqueous solution of PEI containing 100 mM NaCl (pH 7.0) toform a Gly-TBO-PEI-modified interface. A 5 mM aqueous CBA solution wasactivated at room temperature in the presence of 2 mM NHS and 2 mM EDCin 100 mM PBS (pH 7.4) for 2 h. The NHS-modified CBA was then reactedwith the Gly-TBO-PEI-functionalized electrodes at room temperature for 1h, resulting in an amide linkage between the carboxylic acid group ofthe CBA and the amine group of the PEI. The resultingGly-TBO-PEI-CBA-modified electrodes were reacted with a 1 mM solution ofNADH in 100 mM PBS (pH 7.4) for 1 h and washed with water. TheGly-TBO-PEI-NADH-functionalized GCE were reacted with a 4.4 mg mL⁻¹solution of TmMtDH in 100 mM PBS (pH 7.4) for 1 h at room temperatureand cross-linked with 25% (v/v) glutaric dialdehyde in water for 20 min.The resulting TmMtDH-modified electrodes were used fro either thebiocatalytic reduction of fructose or oxidation of mannitol.

The cofactor and enzyme-functionalized PEI layer was removed byincubating the electrode in 10 mM HCl (pH 2.0) at room temperature for30 min. At pH values below the pKa of Gly (pKa˜4.3), the carboxylic acidgroups are protonated, thus decreasing electrostatic attraction betweenthese groups and amine groups of PEI and allowing the TmMtDH-modifiedPEI to disengage from the surface. To reconstitute the interface, PEI,CBA, NADH, and TmMtDH were deposited onto the TBO-modified Gly monolayerusing the protocol described above.

Surface Characterization

Atomic Force Microscopy

The bioelectronic interface's topography and surface roughness weremeasured using a Nanoscope IV multimode atomic force microscope (AFM)(Digital Instruments, Santa Barbara, Calif.) equipped with a “J” (100μm) scanner. Silicon cantilevers (model NSC15/ALBS, resonance frequency300 kHz, force constant 40 N m⁻¹, MicroMasch, Wilsonville, Oreg., USA)were used in tapping-mode at ambient temperature. Atomic forcemicrographs were acquired at scan rates ranging from 0.5 to 1 Hz at ascan angle of 0°. The height data were flattened using a second orderfit. Features were obtained from cross-sectional analysis of the AFMdata.

Ellipsometry

Ellipsometric thickness measurements on amine-terminated silicon waferswere made using a rotating analyzer ellipsometer (model M-44, J. A.Woollam) and WVASE32 software (included with the instrument). Forlayer-by-layer monitoring of growth, films were dried with N₂ afterdeposition of each layer, but in all other cases films were dried onlyafter deposition of the entire film. A film refractive index of 1.5 wasassumed in all thickness determinations.

X-ray Photoelectron Spectroscopy

To verify that electrooxidation can immobilize Gly on the surface of theelectrode, the Gly-modified GCE surface was characterized by XPS (Ma etal., 2005). XPS data were acquired using a Perkin-Elmer PhysicalElectronics PHI 5400 X-ray photoelectron spectrometer equipped with a MgX-ray source operated at 300 W (15 kV, 20 mA). The elementalnitrogen-to-carbon (N/C) ratio was calculated by dividing the totalnumber of counts under the N(1s) band by that under the C(1s) (284.6 eV)band and multiplying the results by 100, after accounting fordifferences in atomic sensitivity factors for each element.

Electrochemical Characterization

A conventional three-electrode cell consisting of the enzyme-modifiedgold working electrode, a platinum auxiliary electrode, and asilver/silver chloride (Ag/AgCl) reference electrode was used forelectrochemical measurements. Electrochemical impedance spectroscopy,chronoamperometry, constant potential amperometry, and cyclicvoltammetry were performed using an electrochemical analyzer (CH1660B,CH Instruments) connected to a personal computer.

Chronoamperometry

Chronoamperometric experiments were conducted by stepping the potentialof the working electrode from 200 mV to −400 mV, triggering thereduction of fructose in the vicinity of the electrode. The redoxreactions that occur simultaneously at the Gly-TBO-PEI-NADHTmMtDH-modified electrode are summarized below:

Origin (Version 7.6, OriginLab, Northampton, Mass.) was used to fitkinetic models to the resulting current vs. time data. Redox componentswith multiple binding modes exhibit a rate constant for each bindingmode. Since NADH has two cis-diol moieties capable of forming a boronicacid linkage during interface formation, a biexponential decay model(Eq. 4) was used to described the current (I) as a function of time (t)(Zayats et al., 2002)I=k′ _(et) Q′ exp(−k′ _(et) t)+k″ _(et) Q″ exp(−k″ _(et) t)+I _(c)  (4)Where, k′_(et) and k″_(et) are the electron transfer rate constants forthe two binding modes Q′ and Q″ are amounts of charge transferred forthe two binding modes. The surface coverage (Γ) of active enzyme can becalculated using Eq. 5 (Zayats et al., 2002), and I_(c) is the chargingcurrent:

$\begin{matrix}{\Gamma = \frac{Q}{nFA}} & (5)\end{matrix}$where F, A, and n are Faraday's constant, electrode area, and the numberof electrons transferred in the reaction (n=2), respectively.Cyclic Voltammetry

Cyclic voltammetric experiments were conducted by sweeping the potentialof the working electrode between 200 mV and −600 mV at a scan rate of100 mV s⁻¹, causing fructose in the vicinity of the electrode to bereduced to mannitol in the positive direction and mannitol to beoxidized to fructose in the reverse direction. All electrochemicalmeasurements were made in 100 mM PBS (pH 6.0) at 60° C. using anelectrode with a controlled surface area of 0.07 cm². The slope of thecalibration plot, which depicts peak current vs. concentration, is ameasure of the biosensor's sensitivity. The maximum turnover rate(TR_(max)), which corresponds to the number of fructose moleculesreduced per TmMtDH molecule per second, was calculated using Eq. 6(Eisenwiener and Schulz, 1969):

$\begin{matrix}{{TR}_{\max} = \frac{I_{cat}^{sat} - I_{o}}{nFA\Gamma}} & (6)\end{matrix}$where the background current (I₀) and saturation current (I_(cat)^(sat)) are given by the y-intercept of the calibration curve and theplateau current at a given concentration, respectively.Electrochemical Impedance Spectroscopy

Electrochemical impedance spectroscopy (EIS) was used to confirmsequential deposition of molecular layers composing the bioelectronicinterface and to examine the electron transfer characteristics on theinterface. Impedance measurements were performed using anelectrochemical analyzer composed of a potentiostat/frequency responsedetector (CHI660B) connected to a personal computer. To follow interfaceassembly, EIS measurements were made in 100 mM PBS (pH 6.0) containing10 mM Fe(CN)₆ ⁻³, 10 mM Fe(CN₆ ⁻⁴, and 10 mM NaCl over six frequencydecades (10⁴ Hz to 10⁻² Hz) at the open circuit potential of the Fe(CN)₆^(−3/−4) solution (221 mV). A modified Randles electrical equivalentcircuit model (Brug et al., 1984) with a solution resistance (R₅),charge transfer resistance (R_(CT)), and constant phase element (CPE)was fit to data using commercial software (Z-view, Version 2.1b,Scribner Associates Inc., Southern Pines, N.C.). The data were displayedas a Nyquist plot [imaginary impedance (Z_(im)) vs. real impedance(Z_(re))].

Several models have been developed to analyze the electrochemicalimpedance spectra of redox polymer films. These models have consideredfurther complexities such as the interaction between redox sites(Armstrong et al., 1986); migration effects (Mathias and Haas, 1992);slow reaction with the soluble species (Bonazzola and Calvo, 1998, Langand Inzelt, 1991); non-uniform film thickness (Mathias and Haas, 1993).However the extensions of the simple interfacial electron transfer anddiffusion charge propagation model have been made at the expense of aless clear physical insight. A simple modified Randles equivalentcircuit was employed that consisted of the ohmic electrolyte resistance(R_(S)) in series with the impedance given by the interfacial doublelayer capacitance (C_(DL)) in parallel to the Faradaic charge transferresistance (R_(CT)) and a finite diffusion impedance (Z_(D)) element. Inthis model, Z_(D) consists of the Warburg parameter (W-R), response time(W-T), and power exponent (W-P). Calvo and Tagliazucchi have developed amodel for electrochemical impedance to study the self-assembly of redoxpolymer modified films; Z_(D) is given by Eq. 7 (Tagliazucchi and Calvo,2007):

$\begin{matrix}{{Z_{D}(\omega)} = {{- {f(\eta)}} = {\frac{1}{C_{F}\omega}\left( \frac{\omega}{\omega_{tr}} \right)^{1/2}j^{1/2}{\coth\left( {\left\lbrack \frac{\omega}{\omega_{tr}} \right\rbrack^{1/2}j^{1/2}} \right)}}}} & (7)\end{matrix}$

where C_(F) is the Faradaic capacitance, ω is the angular frequency,ω_(tr) is the transition frequency, and f(η) is the potential dependenceof the film and given by Eq. 8 (Tagliazucchi and Calvo, 2007):

$\begin{matrix}{{f(\eta)} = {\frac{1}{4}\left\lbrack {{\exp\left( \frac{\eta\; F}{2\;{RT}} \right)} + {\exp\left( {- \frac{\eta\; F}{2{RT}}} \right)}} \right\rbrack}^{2}} & (8)\end{matrix}$

where η, F, R, and T are the apparent overpotential (η=E−E⁰) is definedwith respect to the reference electrode outside the film (Calvo andWolosiuk, 2002), Faraday's constant, the ideal-gas constant, andtemperature, respectively. The apparent diffusion coefficient could bedetermined by (Deng et al., 2007, Tagliazucchi and Calvo, 2007):D _(app)=ω_(tr) d ²  (9)

where D_(app) is the apparent diffusion coefficient of charges in thefilm and d is the film thickness. It is possible to obtain quantitativeinformation on the charge propagation that results from electrontransport through the interface and movement of ions to compensate theelectrical charges.

Results and Discussion

Gly Adsorption

FIG. 1 shows the anodic immobilization of Gly in PBS (pH 7.4) at a scanrate of 100 mV s⁻¹. An oxidation peak observed at 1300 mV in the anodicdirection (FIG. 1) represents the one-electron oxidation of the aminogroup into its corresponding cation radical. The magnitude of this peakincreased with each successive scan, which is consistent with theliterature suggesting the cation radicals form carbon-nitrogen linkagesat the glassy carbon surface. A reduction peak at −420 mV, increasedwith each successive scan. The increases in both the oxidation andreduction peaks suggest that an electroconductive film is formed on theelectrode surface.

The three curves in FIG. 2 show the XPS spectrum of the N1s region forthe freshly polished GCE (Curve 1), GCE after soaking in 100 mM Gly for1 h (Curve 2), and after redox cycling in a 100 mM Gly solution (Curve3). A characteristic N1s peak appears at 399.4 eV, consistent with theformation of a carbon-nitrogen bond between an amine cation radical andan aromatic moiety of the GCE. To check that a strong, most likelycovalent bond was established and that the glycine was not physicallyadsorbed on the surface, the electrode was immersed in 100 mM Gly for 60min. at room temperature and sonicated in water for 10 min. Theresulting XPS spectrum indicated only trace amounts of nitrogen on theelectrode, presumably due to the physical adsorption of the Gly on theGCE. The nitrogen to carbon ratio (N/C) increased from 1.0 for the bareGCE to 1.8 for the electrode soaked in 100 mM Gly, and then to 4.1 forthe electrode that experienced voltage cycling in the presence of Gly,according to the experimental procedure described above. These resultssuggest that voltage cycling resulted in a strong, most likely covalentC—N bond on the electrode.

Interface Assembly

FIG. 3A shows the Faradaic impedance spectra of GCE modified with Gly,Gly-TBO, Gly-TBO-PEI, Gly-TBO-PEI-NADH, and Gly-TBO-PEI-NADH-TmMtDH(Curves 1-5, respectively). The charge transfer resistance increasedwith each subsequent layer, providing evidence of each step in theinterface-formation process. FIG. 3(B) (Curve 1) shows the Nyquist plotfor the Gly-TBO-PEI-NADH-TmMtDH-modified electrodes after being treatedwith 10 mM HCl. The R_(CT) value after HCl treatment (780±0.9 Ωcm²) wasapproximately equal to that for the original Gly-TBO-modified electrode(760±1.0 Ωcm²), suggesting that the HCl treatment removed the NADH- andTmMtDH-modified PEI layers. After neutralizing pH and reabsorbing thePEI, CBA, NADH, and TmMtDH, the R_(CT) increased to 2500±21 Ωcm² [FIG.3(B), Curve 2], a value consistent with the originalGly-TBO-PEI-NADH-TmMtDH-modified electrode (2300±20 Ωcm²). These datasuggest that the NADH-TmMtDH-modified PEI was effectively removed byadjusting pH and then reconstituted.

The surface morphologies of the bare GCE,Gly-TBO-PEI-NADH-TmMtDH-modified electrode before HCl treatment, afterHCl treatment, and after the readsorption of the Gly, TBO, PEI, NADH,and TmMtDH were characterized by AFM in order to investigate thehomogeneity of the film. The root-mean-square (RMS) roughness of theGly-TBO-PEI-NADH-TmMtDH-modified interface (3.26±0.28 nm) has asignificantly different morphology compared to the bare GCE (0.88±0.62nm). The increase in roughness suggests that the Gly, TBO, PEI, NADH,and TmMtDH are bound to the surface of the electrode. Followingtreatment with 10 mM HCl the RMS roughness decreases (1.26±0.27 nm)confirming that material is removed from the surface of the electrode.Upon readsorption of the PEI, NADH, and TmMtDH the RMS roughnessincreased to 3.51±0.92 nm. The measured RMS roughness is consistent withthe adsorption of the original Gly-TBO-PEI-NADH-TmMtDH-interface,suggesting that the PEI, NADH, and TmMtDH were readsorbed onto thesurface of the GCE. The average thickness of the Gly-TBO-PEI-NADH-TmMtDHwas found to be 12.4±1.3 Å. The surface morphology and ellipsomemtricdata are consistent with the EIS data, collectively providing strongevidence that that the Gly-TBO-PEI-NADH-TmMtDH-modified electrode can besuccessfully assembled, removed, and then reassembled on a GCE.

Interface Characterization

Enzyme Adsorption Kinetics

FIG. 4A shows cyclic voltammograms for the Gly-TBO-PEI-NADH-modifiedelectrode in the presence of 250 mM fructose after different times ofTmMtDH adsorption. FIG. 4B shows the peak anodic current at variousadsorption times. A first-order kinetic model was fit to thepeak-anodic-current vs time data, yielding a time constant of 58 min.This value is similar to that obtained for secondary alcoholdehydrogenase adsorption on a cysteine-TBO-NADP⁺-modified interfaceassembled on a gold-coated silicon wafer (43 min).

Scan Rate Effects

The charge transfer dynamics of the Gly-TBO-PEI-NADH-TmMtDH-modifiedelectrode were studied by conducting cyclic voltammetry at scan ratesranging between 25 and 300 mV s⁻¹ in 100 mM PBS (pH 6.0) at 60° C.containing 250 mM fructose [FIG. 5A]. Both the anodic and cathodic peakcurrents increased linearly with scan rate [FIG. 5B], indicating thatthe redox reaction at the film electrode was a surface controlledprocess. Curves 1 through 7 are for increasing scan rates.

pH Effects

The influence of pH on the redox reactions is shown in FIG. 6 for pHvalues of 2 (Curve 1), 4 (Curve 2), 6 (Curve 3), 8 (Curve 4) and 10(Curve 5). The peak cathodic potential (E_(PC)) and peak anodicpotentials (E_(PA)) varied linearly with pH, giving slopes of 63.0 mV(pH unit)⁻¹ for E_(PC) and 65.0 mV (pH unit)⁻¹ for E_(PA). According tothe Nernst equation, the theoretical value of this slope should be 59.16m/n mV (pH unit)⁻¹, where m and n correspond to the number of protonsand electrons transferred during oxidation, respectively. The closenessof this value to the experimentally obtained slopes suggests that anequal number of electrons and protons are exchanged during the anodicand cathodic sweeps, respectively.

Apparent Diffusion Coefficient

FIG. 7 shows the frequency dependence of the impedance for theGly-TBO-PEI-NADH-TmMtDH-modified GCE. At formal potential, theGly-TBO-PEI-NADH-TmMtDH-modified GCE displayed two distinct regions, aspredicted by the finite line model of Albrey (Albery et al., 1990). Thisbehavior is consistent with those of other redox polymer systems(Musiani, 1990). Fitting the spectrum to the equivalent circuit in thelower inset of FIG. 7, yielded best fit values for R_(S), C_(DL), W-R,W-T and W-P of 137±17.0Ω, 8.79±0.96×10⁻⁸ F, 6.8±4.8×10⁴Ω, 48.6±0.75 sand 0.86±0.05, respectively. The transition frequency was determined tobe 4.6±0.7×10³ Hz. The charge diffusion coefficient through theGly-TBO-PEI-NADH-TmMtDH-modified GCE was 1.03±0.26×10⁻¹⁰ cm² s⁻¹. TheD_(app) value is comparable to other supermolecular architectures inwhich a conductive polymer is used for mediated electron transfer(Ochmanska and Pickup, 1991, Pickup et al., 1984). Polymer layers areknown to swell when placed in an electrolyte solution (Itano et al.,2005), suggesting the actual D_(app) value might be slightly larger thanthat estimated above.

The calculated D_(app) value should be considered a binary diffusioncoefficient since both the TBO_(OX)/TBO_(RED) centers could beresponsible for the charge transfer inside the film, via electronhopping and counter ion diffusion (Tagliazucchi and Calvo, 2007). Whenthe diffusion is ion-limited the high frequency resistance (R_(∞))becomes infinite at potentials far from the oxidation potential of theredox species (Mathias and Haas, 1993). However, if the diffusion islimited by electron hoping, R_(∞) is independent of the appliedpotential (Tagliazucchi and Calvo, 2007). For theGly-TBO-PEI-NADH-TmMtDH-modified electrode, R_(∞), measured at 10 kHzvaries about 10 Ωcm² in the potential range −300 mV to 0 mV, indicatingthat the ion transport is fast therefore D_(app) is the apparentdiffusion coefficient for electron hoping.

Surface Properties

FIG. 8 shows the chronoamperometric current response for theGly-TBO-PEI-NADH-TmMtDH-modified electrode following a step change inpotential from 100 to −600 mV measured in 100 mM PBS (pH 6.0) atcontaining 250 mM fructose at 60° C. Fitting Eq. 4 to thechronoamperometric data gave k′_(et) and k″_(et) values of 281.3±1.5 and103.7±1.9 s⁻¹ suggesting that the NADH binds to phenylboronic acidthrough both of the possible ligation modes. The differences in electrontransfer coefficient indicating that one of the twoCBA-NADH-TmMtDH-complexes transfers electrons about twice as fast theother. The Γ values for bioelectronic complexes possessing the twoligation modes were determined to be 1.1±0.2×10⁻¹¹ and 1.0±0.1×10⁻¹¹ molcm⁻² using Eq. 5.

FIG. 9(A) shows the cyclic voltammograms of theGly-TBO-PEI-NADH-TmMtDH-modified electrode at various fructoseconcentrations in 100 mM PBS (pH 6.0) at 60° C. The peak current variedlinearly with fructose concentration [FIG. 9(B)] demonstrating that theinterface could be used as a fructose biosensor. The slope of thecalibration curve (0.70±0.01 μA) mM⁻¹ cm⁻²) is a measure of thebiosensor's sensitivity. At higher concentrations, the anodic currentreached a saturation value (I_(cat) ^(sat)=740.9±11.6 μA cm⁻²). Thisvalue was used to calculate a TR_(max), which represents the number ofmolecules of fructose reduction per TmMtDH molecule per second, of57.5±2.8 s⁻¹, using Eq. 6 (Eisenwiener and Schulz, 1969). TheGly-TBO-PEI-NADH-TmMtDH-modified electrode exhibited 10% loss inactivity upon operation for 24 h at 60° C. Following storage at roomtemperature in 100 mM borate buffer (pH 7.0) theGly-TBO-PEI-NADH-TmMtDH-modified interface exhibited a 50% activity lossafter 14 days.

The selectivity of the Gly-TBO-PEI-NADH-TmMtDH-modified electrode wasexamined by testing alternative substrates. Table 2 shows thesensitivity and turnover rate of the Gly-TBO-PEI-NADH-TmMtDH-modifiedelectrode to fructose, glucose, arbinose, and sorbose. These data areconsistent with the literature values for TmMtDH, indicating that theelectrode has little activity for sugars besides fructose (Song et al.,2008).

TABLE 2 I_(cat) ^(sat) Sensitivity Compound (μA cm⁻²) (μA mM⁻¹ cm⁻²)Fructose  748.2 ± 11.7 10.1 ± 0.2  Glucose 530.7 ± 2.2 0.2 ± 0.0 Sorbose562.4 ± 1.4 0.4 ± 0.0 Arbinose 542.8 ± 9.1 0.3 ± 0.0

To confirm reviewability of the interface, the performance properties ofthe Gly-TBO-PEI-NADH-TmMtDH-modified electrode were measured before andafter interface removal by HCl wash and reconstitution of the PEI, NADH,and TmMtDH. The values of Γ, k_(et), I_(cat) ^(sat), sensitivity, andTR_(max) for the reconstituted Gly-TBO-PEI-NADH-TmMtOH-modifiedelectrode were virtually identical to those for theGly-TBO-PEI-NADH-TmMtDH-modified electrode-modified electrode containingfour cassettes before HCl treatment, suggesting that the interface couldbe removed and reconstituted without loss in performance.

The novel approach presented here uses functionalized polyelectrolytesto fabricate bioelectronic interfaces on GCEs that can be removed by asimple pH change and then reconstituted. The ability to reconstitutedehydrogenase-based bioelectronic interfaces without affectingperformance can greatly reduce the operating costs of bioelectronicprocesses. The PEI, NADH, and TmMtDH can be removed by a decrease in pHand then reconstituted by passing PEI, NADH, and TmMtDH over theelectrode. The Gly-TBO-PEI-NADH-TmMtDH-modified electrode has severalpotential applications including bioreactors and biofuel cells.

To assemble the bioelectronic interface, an electron mediator was firstcovalently bound to a GCE, followed by adsorption of a positivelycharged polyelectrolyte functionalized with its cofactor. Finally theenzymes were adsorbed by electrostatic interactions. AFM,chronoamperometry, cyclic voltammetry, EIS, and XPS were used todemonstrate sequential assembly of the layers and to characterize theperformance of the resulting bioelectronic interfaces. The labilecomponents of the interface could be removed by a decrease in pH andthen reconstituted to regenerate the functional bioelectronic interface.The sensitivity, I_(cat) ^(sat), and TR_(max) of the reconstitutedinterface (0.7±0.1 μA mM⁻¹ cm⁻², 734.2±16.9 μA cm⁻², and 52.1±4.2 s¹,respectively) were comparable to those of the original (0.7±0.0 μA mM⁻¹cm⁻², 740.9±11.6 μA cm⁻², and 57.5±2.8 s⁻¹, respectively). The abilityto develop a bioelectronic interface on a GCE has potential applicationsfor biosensors and biocatalytic reactors (FIG. 1A), and biological fuelcells.

In accordance with certain embodiments of the invention, a bioelectronicinterface containing exfoliated nanographite supports (e.g., exfoliatedgraphite nanoplatelets) modified with a polyelectrolyte may be employedto achieve increased enzymatic surface coverage (e.g., from about2.1×10⁻¹¹ to about 3.3×10⁻¹¹ moles per square centimeter) as comparedwith known bioelectronic interfaces leading to improved sensitivity,saturation current, and turnover rate (e.g., about 5.5 μA mM⁻¹ cm⁻²,about 185 μA cm⁻², and 24 s⁻¹, respectively). As an alternative, carbonnanotubes, fullerenes, and the like may be used rather than exfoliatedgraphite. The use of a polyelectrolyte allows the interface to beremoved via a pH change to facilitate regeneration of a new interface onan electrically conductive carbon electrode. An example application thisapproach using is described below.

The incorporation of the exfoliated graphite, carbon nanotubes, and/orfullerenes into polyelectrolyte films is significant due to their uniquechemical, physical, and electronic properties. The research group of Dr.Larry Drzal has developed a process to produce exfoliated graphitenanoplatelets (xGnP™) that range in thickness between 1 nm and 10 nm anddiameter between 100 nm and 1000 nm. The chemical, physical, andelectronic properties are consistent with carbon nanotubes andfullerenes. The cost of production ($5/pound) makes the xGnP a suitablereplacement for carbon nanotubes and fullerenes. xGnP has recently beendispersed in sodium dodecylbenzene sulfonate (SDBS), sodium dodecylsulfate (SDS), sulfated poly(styrene) (SPS), poly(acrylic acid) (PAA),poly(diallyldimethylammonium chloride) (PDAC) and polyethyleneimine(PEI). Coating xGnP with charged polymers increases both the stabilityof the suspension and the surface charge of the xGnP, making it possibleto self assemble in layer-by-layer (LbL) films.

A novel assembly method which incorporates polyelectrolyte-modified xGnPinto polyelectrolyte multilayers (PEMs) can be used for the fabricationof renewable bioelectronic interfaces. PEI was used to couple the xGnP,cofactor, and enzyme to a mediator-modified electrostaticallyfunctionalized electrically conductive carbon electrode in such a waythat efficient electron transfer was achieved.

Escherichia coli (DH5αpADH B1M1-kan) culture containing a recombinantplasmid for secondary alcohol dehydrogenase (2° ADH) fromThermoanaerobacter ethanolicus was grown and purified in accordance withknown techniques.

Tryptone, yeast extract, dithiothreitol, kanamycin, and ampicillin wereobtained from Fisher Scientific (Pittsburgh, Pa.). All other chemicals,including cysteine, 1-ethyl-3-(3-dimethylaminopropyl) carbodiimide(EDC), n-hydroxysuccinimide (NHS), toluidine blue O (TBO),polyethyleneimine (PEI), 3-carboxy phenylboronic acid (CBA),β-nicotinamide adenine dinucleotide phosphate (NADP⁺), glutaricdialdehyde (10% in water), 2-propanol, ethanol, 2-butanol, 2-pentanol,potassium ferrocyanide, and potassium ferricyanide were obtained fromSigma-Aldrich (St. Louis, Mo.). Ultrapure water (18.2 MΩ) was obtainedfrom a Barnstead Nanopure-UV four-stage purifier (BarnsteadInternational, Dubuque, Iowa).

A 0.1 g sample of xGnP was dispersed in a 1 g L⁻¹ aqueous PEI solutioncontaining 0.1 M NaCl (pH 7.0). The graphite dispersion wastip-sonicated using a Branson B15 (Branson Ultrasonic Corporation,Danbury, Conn.) sonication immersion tip (100 W, pulsed) for 30 minfollowed by stirring for 24 h. The PEI coated xGnP were then filteredusing a 0.22 □m Millipore filter (Millipore, Billerica, Mass.) andwashed three times with deionized water, filtering after each washingstep. The xGnP was then collected and redispersed in 100 mL DI waterusing mild tip sonication (50 W, pulsed) for 10 min.

Glassy carbon electrodes may be treated in a manner that imparts acharge on the surface, thereby facilitating binding of polyelectrolytes.In the embodiment described below, the GCE was immersed in cysteine, andthe electrical potential of the GCE was cycled. This process is believedto oxidize cysteine's amino acid group, leading to a cationic nitrogenradical that forms a carbon-nitrogen bond on the surface of the GCE.

The cysteine-modified gold electrodes were incubated for 2 h in 100 μMTBO in a 0.1 M phosphate buffer solution (PBS) (pH 7.4) in presence of 2mM NHS and 2 mM EDC, resulting in the formation of an amide linkagebetween TBO and the carboxyl group of the cysteine (MPA-TBO). Thecysteine-TBO-modified electrodes were soaked in a 10 mM aqueous PEI/xGnPsolution (pH 7.0) forming a cysteine-TBO-PEI/xGnP-modified interface. A5 mM aqueous CBA solution was activated at room temperature in thepresence of 2 mM NHS and 2 mM EDC in PBS (pH 7.4) for 2 h. TheNHS-modified CBA was then reacted with thecysteine-TBO-PEI/xGnP-functionalized electrodes for 1 h at roomtemperature, resulting in an amide linkage between the CBA and the aminegroup of the PEI. The resulting cysteine-TBO-PEI/xGnP-CBA-modifiedelectrodes was reacted with a 1 mM solution of NADP⁺ in 0.1 M PBS (pH7.4) for 1 h and then washed with water. Thecysteine-TBO-PEI/xGnP-NADP⁺-functionalized GCEs were reacted with a 4.4mg mL⁻¹ solution of 2° ADH in 0.1 M PBS (pH 7.4) for 1 h at roomtemperature and cross-linked with 10% (v/v) glutaric dialdehyde in waterfor 20 min. The resulting 2° ADH-modified interfaces were used for thebiocatalytic oxidation of 2-propanol.

The functionalized PEI-modified xGnP was removed by incubating theelectrode in 0.01 M HCl (pH 2.0) for 30 min. Under these conditions, thecarboxylic acid groups of the cysteine become protonated, thusdecreasing the electrostatic interaction between the surface boundcysteine and the PEI. The decrease in electrostatic interaction allowsthe PEI to disengage from the surface. To reassemble the interface,PEI-modified xGnP, CBA, NADP⁺, and 2° ADH can then be readsorbed usingthe protocol described above.

xGnPs may also be grafted onto a reticulated vitreous carbon (RVC)surface to increase surface area. One grafting method involves firstassembling TBO molecules onto the carbon nanoparticles, followed bybinding the TBO/carbon nanoparticle adduct on the RVC. This approachprovides a high surface area, TBO/carbon composite electrode thatreduces the NADH oxidization overpotential compared to bare carbonelectrodes. In another approach, a Polyelectrolyte multilayer (PEM) baselayer may be adsorbed directly onto the carbon, and otherpolyelectrolyte layer(s) functionalized with a mediator, cofactor, andenzyme may then be absorbed. A variety of carbon electrode substratematerials may be used, including GCE and RVC. The bioelectronicinterface assembly methods would be substantially the same methods foreach, although some optimization may be needed for each electrodematerial.

In accordance with another embodiment of the invention, a renewablebioelectronic interface utilizing multiple nanostructured bioelectroniccassettes that are stacked in series to form bioelectronic interfaceshaving higher reaction capacities may also be utilized in thebiocatalytic reactor 1 (FIG. 1A). The multilayered bioelectroniccassettes may be formed on carbon electrodes such as a GCE that mayoptionally include exfoliated graphite nanoplatelets or othercarbon-based structures to increase the surface area, including carbonnanotubes, carbon black, graphite, and fullerenes. The techniquesdescribed in detail above to form an initial interface on a GCEsubstrate may be utilized to form an initial layer on various carbonsubstrates.

The polyanionic poly(acrylic acid) (PAA) and polycationicpoly(ethyleneimine) (PEI) have been used for directed self-assembly ofcassettes containing a mediator (toluidine blue O, [TBO]), a cofactor(NADP⁺), and an enzyme (thermostable secondary alcohol dehydrogenase [2°ADH]) onto a carboxylic-acid-modified carbon electrode orelectrostatically functionalized carbon electrode. However, a variety ofother polyanionic and polycationic molecules may optionally be usedinstead to achieve mediated electron transfer within each cassette andacross multiple cassettes in series.

In the multi-cassette embodiment described below, the secondary alcoholdehydrogenase (2° ADH) from Thermoanaerobacter ethanolicus was producedusing recombinant Escherichia coli (DH5αpADH B1M1-kan) and then purifiedin accordance with known techniques.

1-ethyl-3-(3-dimethylaminopropyl) carbodiimide (EDC),n-hydroxysuccinimide (NHS), TBO, polyethyleneimine (PEI), poly(acrylicacid) (PAA), 3-carboxy phenylboronic acid (CBA), 3-nicotinamide adeninedinucleotide phosphate (NADP⁺), glutaric dialdehyde (25% in water),2-propanol, ethanol, 2-butanol, 2-pentanol, were obtained fromSigma-Aldrich (St. Louis, Mo.). Ultrapure water (18.2 MΩ) were obtainedfrom a Barnstead Nanopure-UV four-stage purifier (BarnsteadInternational, Dubuque, Iowa).

Electrically conductive carbon electrodes were treated with cysteine ina manner to covalently bind the cysteine to the carbon electrodes. Thisapproach uses potential cycling to oxidize cysteine's amino group to acationic radical, which forms a carbon-nitrogen bond with the carbonelectrode. The cysteine-modified carbon electrodes were incubated tor 2h in 0.1 mM TBO in a 100 mM phosphate buffer solution (PBS) (pH 7.4) inthe presence of 2 mM NHS and 2 mM EDC, resulting in an amide linkagebetween the TBO and the cysteine. The cysteine-TBO-modified electrodeswere immersed in a 10 mM aqueous PEI solution containing 100 mM NaCl (pH7.0), forming a cysteine-TBO-PEI-modified interface. A 5 mM aqueous CBAsolution was activated at room temperature in the presence of 5 mM NHSand 5 mM EDC in 100 mM PBS for 2 h. The NHS-modified CBA was thenreacted with the cysteine-TBO-PEI-functionalized electrodes for 1 h atroom temperature. The resulting cysteine-TBO-PEI-CBA-modified electrodeswas immersed in a 1 mM solution of NADP⁺ in 100 mM PBS for 1 h and thenwashed with water. To bind 2° ADH, thecysteine-TBO-PEI-NADP⁺-functionalized carbon electrodes were immersed ina 4.4 mg mL⁻¹ solution of 2° ADH in 100 mM PBS for 1 h at roomtemperature. This step completes the fabrication of the firstbioelectronic cassette, yielding a fully functionalcysteine-TBO-PEI-NADP⁺-2° ADH bioelectronic interface.

To add additional cassettes on top of the first, the 2° ADH-terminatedinterfaces were immersed in a 10 mM aqueous PEI solution containing 100mM NaCl (pH 7.0), and washed with water to remove the residual PEI fromthe surface. The resulting PEI-modified electrodes were immersed in a100 mM PAA solution (pH 5.5) and washed with water. Thecysteine-TBO-PEI-NADP⁺-2° ADH-PEI-PAA-modified electrodes were incubatedfor 2 h in 0.1 mM TBO in a 100 mM PBS in the presence of 2 mM NHS and 2mM EDC, resulting in the formation of an amide linkage between the TBOand the PAA. The electrodes were then immersed in a 10 mM aqueous PEIsolution (pH 7.0). The NHS-activated CBA was then reacted withcysteine-TBO-PEI-NADP⁺-2° ADH-PEI-PAA-TBO-PEI-functionalized electrodesfor 1 h at room temperature. The resulting CBA-modified electrodes werereacted with a 1 mM NADP⁺ solution in 100 mM PBS for 1 h and then washedwith water. The second cassette was completed by immersing theelectrodes in a 4.4 mg mL⁻¹ 2° ADH solution in 100 mM PBS for 1 h atroom temperature. The assembly process described above for the secondcassette was carried out n times to add n PAA-TBO/PEI-NADP⁺-2° ADHfunctional units on top of the first cassette, resulting in a total ofn+1 bioelectronic cassettes in series. The resulting interface isdescribed as a cysteine-TBO-PEI-NADP⁺-2° ADH-[PAA-TBO/PEI-NADP⁺-2°ADH]_(n)-modified interface.

The labile components of the interface were removed by incubating theelectrode in 10 mM HCl (pH 2.0) for 30 min. At pH values below the pKaof MPA (pKa˜4.3), the carboxylic acid group was protonated, thusdecreasing the electrostatic interaction between the surface boundcysteine and the modified PEI and allowing the PEI to disengage from thesurface. To reassemble the interface, the PEI, CBA, NADP⁺, PAA, TBO, and2° ADH were reattached onto the TBO-modified MPA monolayer using theprotocol described above.

To optimize the performance properties of a bioreactor for eachenzyme/reactant system, a variety of mediators, cofactors, and carbonelectrode materials may be utilized. Furthermore, reactor geometry,liquid residence time, applied voltage, temperature, pH, etc. mayadjusted to optimize performance for each system. A mathematical modelthat may be utilized in designing bioreactor 1 is described herein.

To optimize the performance of enzyme-based bioelectronic interfaces itis necessary to understand the relationship among the substrate/producttransport, electron transport, and enzyme kinetics.

The mathematical models of those relationships result in highlynon-linear differential equations. Both numerical solutions to theentire model and analytical solutions to simplified versions of themodel have been developed for these problems.

A variety of numerical techniques including explicit finite difference(Jemmer, 1999) and Crank Nicholson (Bergel and Comtat, 1984) have beenused to solve both transient and steady-state problems with a variety ofdifferent boundary conditions. Analytical solutions generally rely onthe identification of suitable limiting cases is which the diffusionkinetic, and reaction equations can be linearized and solved. Thisapproach has been used to analyze the kinetics of reaction at apolymer-modified electrode in which the species from solution reactswith a mediator bound within a film found at the electrode surface(Andrieux et al. 1982, Rahamathunissa and Rajendran, 2008, Scott andBowden, 1994. Bartlett and Pratt developed numerical simulations tovalidate their analytical solutions to limiting cases of the model andto investigate the boundary regions between the different limiting cases(Bartlett and Pratt, 1995). However, these models have not been extendedto enzyme systems with reversible kinetics.

We develop a model that extends the approach of Bartlett and Pratt toinclude bioelectronic interfaces having reversible enzymes, cofactors,and mediators. The model's predictions were verified with experimentalresults. The general approach developed takes into account reversibleenzyme kinetics, mediator kinetics, substrate diffusion, productdiffusion, and electron diffusion. To simplify the treatment, we excludethe effects of mass transport in solution outside the film. The model isrestricted to steady state, and is limited to the case where the enzymeand electron mediator are bound within the film. The electrochemicalbehavior of the bioelectronic interface was characterized usingchronoamperometry and compared with the model predictions. The analystspresented here could be used to design and optimize conditions forbiofuel cell, biocatalysis, and biosensing applications.

FIG. 10, shows the kinetic scheme for an enzyme-modified electrode(Bartlett and Pratt, 1995) based on a redox enzyme which follows anordered bi-bi mechanism. In FIG. 10, S and P represent the substrate(reduced species) and product (oxidized species), respectively, E₁ andE₂ represent the reduced and oxidized forms of the enzyme/cofactorcomplex, respectively, and M₁ and M₂ represent the oxidized and reducedforms of the mediator, respectively. The enzyme is assumed to beimmobilized in the film such that the concentration is uniformthroughout the thickness (l) of the film. The substrate and the productare free to diffuse through the film with diffusion coefficients ofD_(P) and D_(S), respectively. Partitioning of the substrate and productacross the solution/membrane interface occurs, with partitioningcoefficients of K_(S) and K_(P), respectively. We will only consider thesituation where the mediator is covalently bound within the film andinteracts with the enzyme reaction directly. Since the mediator is boundwithin the film the mediator diffusion coefficient (D_(M)) correspondsto the diffusion of charge through the matrix rather than the physicaldiffusion of the mediator.

The ordered bi-bi reaction of the enzyme with the substrate and cofactoris shown in Eq. (10):

where k₁ and k⁻¹ are the reaction rate constants describing the reactionof the enzyme (E) and the reduced cofactor (C₁) to form anenzyme/reduced cofactor complex (EC₁). k₁ and k₂ are the rate constantsdescribing the reaction of EC₁ and substrate (S) to form theenzyme/cofactor/substrate (EC₁S). k₃ and k⁻³ are the rate constants forthe breakdown of EC₁S into enzyme/oxidized cofactor complex (EC₂) andproduct (P). k₄ and k⁻⁴ are the reaction rate constants describing thebreakdown of EC₂ into E and the oxidized cofactor (C₂). z_(S) and z_(B)represent the stoichiometric coefficients of the substrate and theproduct, respectively, with respect to amount of the enzyme involved inthe reaction, where the cofactor stoichiometry is assumed to be one. Itis assumed that the enzyme and cofactor are directly bound within thefilm, indicating that the association and dissociation rate constantsfor EC₁ and EC₂ (k₁, k⁻¹, k₄, and k⁻⁴) are negligible compared the rateconstants for the enzyme reaction, suggesting Eq. (10) can be simplifiedto Eq. (11).

The other reaction within the film can be written as:

where k_(A) and k_(B) are the forward and reverse rate constantsdescribing the reaction of the mediator (M₁/M₂) with EC₁ and EC₂. z_(M)is the stoichiometric coefficient for the mediator with respect to theenzyme. The reaction at the electrode surface is give as Eq. (13).M₂

M₁  (13)The rate of this reaction is assumed to be to be fast relative to theenzyme reaction, so it is always in equilibrium. The rate of reactionwith respect to product formation (ν_(p)) can be written as:νp=k ₃ [EC ₁ S]−k ⁻³ [EC ₂ ][P] ^(z) ^(p)   (14)The reaction rates with respect to the substrate and mediator arerelated by stoichiometry which can be expressed as:

$\begin{matrix}{v_{P} = {{{- \left( \frac{z_{S}}{z_{P}} \right)}v_{S}} = {{- \left( \frac{z_{M}}{z_{P}} \right)}v_{M}}}} & (15)\end{matrix}$where ν_(S) and ν_(M) are the reaction rates with respect to thesubstrate and the electron mediator, respectively. For simplicity, herewe assume that z_(S), z_(P), and z_(M) are equal to 1. We can write thefollowing partial differential equations describing diffusion andreaction within the film:

$\begin{matrix}{\frac{\partial\lbrack S\rbrack}{\partial t} = {{D_{S}\frac{\partial^{2}\lbrack S\rbrack}{\partial x^{2}}} - v_{S}}} & (16) \\{\frac{\partial\lbrack P\rbrack}{\partial t} = {{D_{P}\frac{\partial^{2}\lbrack P\rbrack}{\partial x^{2}}} - v_{P}}} & (17) \\{\frac{\partial\left\lbrack M_{1} \right\rbrack}{\partial t} = {{D_{M}\frac{\partial^{2}\left\lbrack M_{1} \right\rbrack}{\partial x^{2}}} - v_{M}}} & (18) \\{\frac{\partial\left\lbrack {{EC}_{1}S} \right\rbrack}{\partial t} = {{{k_{2}\lbrack S\rbrack}\left\lbrack {EC}_{1} \right\rbrack} - {k_{- 2}\left\lbrack {{EC}_{1}S} \right\rbrack} - {v_{P}\mspace{14mu}{and}}}} & (19) \\{\frac{\partial\left\lbrack {EC}_{2} \right\rbrack}{\partial t} = {v_{P} - {{k_{A}\left\lbrack M_{1} \right\rbrack}\left\lbrack {EC}_{2} \right\rbrack} + {{k_{3}\left\lbrack M_{2} \right\rbrack}\left\lbrack {EC}_{1} \right\rbrack}}} & (20)\end{matrix}$It can be assumed that the enzyme is bound within the film and is notfree to diffuse and assuming steady-state conditions, ∂[EC₁S]/∂t=0.Introducing [E_(T)]=[EC₁]+[EC₂]+[EC₁S] and [M_(T)]=[M₁]+[M₂] are thetotal concentration of immobilized enzyme and mediator, respectively.

[EC₁S] can be expressed as Eq. (21):

$\begin{matrix}{\left\lbrack {{EC}_{1}S} \right\rbrack = \frac{{{k_{2}\lbrack S\rbrack}\left\lbrack E_{T} \right\rbrack} + {\left\lbrack {EC}_{2} \right\rbrack\left( {{k_{- 3}\lbrack P\rbrack} - {k_{2}\lbrack S\rbrack}} \right)}}{\left( {k_{- 2} + k_{3} + {k_{2}\lbrack S\rbrack}} \right)}} & (21)\end{matrix}$Substituting Eq. (21) into Eq. (20) and solving for [EC₂].

$\begin{matrix}{{\left\lbrack {EC}_{2} \right\rbrack = \frac{k_{3}{k_{b}\left\lbrack {{M_{2}\left\lbrack E_{T} \right\rbrack} + {k_{- 2}{{k_{b}\left\lbrack M_{2} \right\rbrack}\left\lbrack E_{T} \right\rbrack}} + {k_{2}{{k_{3}\lbrack S\rbrack}\left\lbrack E_{T} \right\rbrack}}} \right.}}{\begin{matrix}{{\lbrack S\rbrack\left( {{k_{2}k_{3}} + {k_{2}{k_{a}\left\lbrack M_{1} \right\rbrack}}} \right)} + {\lbrack P\rbrack\left( {{k_{- 3}{k_{b}\left\lbrack M_{2} \right\rbrack}} + {k_{- 2}k_{- 3}}} \right)} +} \\{{k_{2}{{k_{- 3}\lbrack S\rbrack}\lbrack P\rbrack}} + {\left( {{k_{a}\left\lbrack M_{1} \right\rbrack} + {k_{b}\left\lbrack M_{2} \right\rbrack}} \right)\left( {k_{- 2} + k_{3}} \right)}}\end{matrix}}}\mspace{20mu}{Substituting}\mspace{14mu}{{Eqs}.\mspace{11mu}(21)}\mspace{14mu}{and}\mspace{14mu}(22)\mspace{14mu}{into}\mspace{14mu}{{Eq}.\mspace{11mu}(14)}\text{:}} & (22) \\{v_{P} = \frac{\left\lbrack E_{T} \right\rbrack\left( {{k_{2}k_{3}{{k_{a}\left\lbrack M_{1} \right\rbrack}\lbrack S\rbrack}} - {k_{- 2}k_{- 3}{{k_{b}\left\lbrack M_{2} \right\rbrack}\lbrack P\rbrack}}} \right)}{\begin{matrix}{{\lbrack S\rbrack\left( {{k_{2}k_{3}} + {k_{2}{k_{a}\left\lbrack M_{1} \right\rbrack}}} \right)} + {\lbrack P\rbrack\left( {{k_{- 3}{k_{b}\left\lbrack M_{2} \right\rbrack}} + {k_{- 2}k_{- 3}}} \right)} +} \\{{k_{2}{{k_{- 3}\lbrack S\rbrack}\lbrack P\rbrack}} + {\left( {{k_{a}\left\lbrack M_{1} \right\rbrack} + {k_{b}\left\lbrack M_{2} \right\rbrack}} \right)\left( {k_{- 2} + k_{3}} \right)}}\end{matrix}}} & (23)\end{matrix}$assuming steady state, Eqs. (16), (17), and (18) become:

$\begin{matrix}{{D_{S}\frac{\partial^{2}\lbrack S\rbrack}{\partial x^{2}}} = v_{S}} & (24) \\{{D_{P}\frac{\partial^{2}\lbrack P\rbrack}{\partial x^{2}}} = v_{P}} & (25) \\{{D_{M}\frac{\partial^{2}\left\lbrack M_{1} \right\rbrack}{\partial x^{2}}} = v_{M}} & (26)\end{matrix}$

Introducing the following dimensionless variables:

$\begin{matrix}{s = \frac{\lbrack S\rbrack}{{K_{S}\lbrack S\rbrack}_{\infty}}} & (27) \\{p = \frac{\lbrack P\rbrack}{{K_{P}\lbrack P\rbrack}_{\infty}}} & (28) \\{m = \frac{\left\lbrack M_{1} \right\rbrack}{\left\lbrack M_{T} \right\rbrack}} & (29) \\{\chi = \frac{x}{l}} & (30) \\{K = \frac{k_{B}}{k_{A}}} & (31) \\{\mu = \frac{k_{2}{K_{S}\lbrack S\rbrack}_{\infty}}{k_{- 2} + k_{3}}} & (32) \\{\lambda = \frac{k_{- 3}{K_{P}\lbrack P\rbrack}_{\infty}}{k_{- 2} + k_{3}}} & (33) \\{\kappa^{2} = \frac{{{k_{A}\left\lbrack E_{T} \right\rbrack}\left\lbrack M_{T} \right\rbrack}l^{2}}{D_{A}{K_{P}\lbrack P\rbrack}_{\infty}}} & (34) \\{\omega = \frac{k_{3}}{k_{A}\left\lbrack M_{T} \right\rbrack}} & (35) \\{\rho = \frac{k_{- 2}}{k_{A}\left\lbrack M_{T} \right\rbrack}} & (36) \\{\alpha = \frac{D_{A}}{D_{P}}} & (37) \\{\beta = \frac{D_{A}}{D_{S}}} & (38) \\{A = \frac{z_{M}{K_{P}\lbrack P\rbrack}_{\infty}}{z_{P}\left\lbrack M_{T} \right\rbrack}} & (39) \\{B = \frac{z_{S}{K_{P}\lbrack P\rbrack}_{\infty}}{z_{P}{K_{S}\lbrack S\rbrack}_{\infty}}} & (40)\end{matrix}$where s, p, and m are the dimensionless concentrations of the substrate,product, and mediator, respectively, normalized with respect to thetotal concentrations of substrate (K_(S)[S]_(∞)), product(K_(P)[P]_(∞)), and mediator ([M_(T)]) within the film, where subscript∞ denotes the concentration in the bulk. The variables K_(S) and K_(P)represent the partition coefficients for the substrate and product,within the film. The normalized distance from the electrode isrepresented by χ. K denotes the ratio of mediator reaction rates, μ andλ represent the ratios of the substrate and product speciesconcentration to the Michaelis-Menten constant for the substrate andproduct, respectively, κ describes the balance between the diffusionwithin the film and its reaction with the enzyme, ω and ρ denote theratio of the forward and reverse enzyme reaction rate, respectively, αand β are the ratios of substrate diffusion and product diffusivity,respectively, to mediator diffusivity. Finally, A is the stoichiometricratio of substrate and mediator concentrations, and B is thestoichiometric ratio of product to mediator concentrations.

Substituting Eqs. (27) through (40) into Eq. (23) gives:

$\begin{matrix}{v_{P} = \frac{k^{2}{\alpha\left( {{s\;{\mu\omega}\; m} - {p\;{\lambda\rho}\;{K\left( {1 - m} \right)}}} \right)}}{\;\begin{matrix}{{s\;{\mu\left( {\omega + m} \right)}} + {p\left( {{\lambda\;{K\left( {1 - m} \right)}} + {p\;\lambda}} \right)} + {{ps}\;{\mu\lambda}\left( {\omega + \rho} \right)} + m +} \\{K\left( {1 - m} \right)}\end{matrix}}} & (41)\end{matrix}$Eqs. (24) through (26) become:

$\begin{matrix}{\frac{\partial^{2}m}{\partial\chi^{2}} = {\left( \frac{A}{\alpha} \right)v_{P}}} & (42) \\{\frac{\partial^{2}s}{\partial\chi^{2}} = {\left( \frac{B\;\beta}{\alpha} \right)v_{P}}} & (43) \\{\frac{\partial^{2}p}{\partial\chi^{2}} = v_{P}} & (44)\end{matrix}$Eqs. (42) through (44) can be solved with the appropriate boundaryconditions.

The substrate and the product are free to diffuse through the film withdiffusion coefficients of D_(P) and D_(S), respectively. Partitioning ofthe substrate and product across the solution/membrane interface occurs,with partitioning coefficients of K_(S) and K_(P), respectively aregiven by Eqs. (45).s| _(χ=1) =p| _(χ=1)=1   (45)The diffusive flux of the product and substrate at the electrode/filminterface is zero, leading to Eqs. (46).

$\begin{matrix}{{{{\frac{\partial s}{\partial\chi}}_{\chi = 0} = \frac{\partial p}{\partial\chi}}}_{\chi = 0} = 0} & (46)\end{matrix}$Useful mechanistic information about the interaction of the substrate,product, and the mediator with the enzyme can be obtained by examiningthe potential dependence of the electrochemical reaction of the mediatorat the electrode surface. We can assume that it remains in equilibriumand apply the Nernst equation:

$\begin{matrix}{E = {E^{0} + {\frac{RT}{n\; F}\ln\frac{\left\lbrack M_{1} \right\rbrack_{0}}{\left\lbrack M_{2} \right\rbrack_{0}}}}} & (47)\end{matrix}$where [M₁]₀ and [M₂]₀ are the concentrations of the two forms of themediator at the electrode surface. E and E⁰ are the applied potentialand the reversible potential for the bound mediator, respectively. R, T,n, and F are the gas constant temperature, electron stoichiometriccoefficient, and Faraday's constant, respectively.

A dimensionless potential (ε) can be defined as:

$\begin{matrix}{ɛ = \frac{\left( {E - E^{0}} \right)n\; F}{RT}} & (48)\end{matrix}$Substituting Eq. (47) into Eq. (48) gives the boundary conditions forthe dimensionless oxidized mediator concentration (m_(c)) at theelectrode surface.

$\begin{matrix}{m_{ɛ} = \frac{1}{1 + {\exp\left( {- ɛ} \right)}}} & (49)\end{matrix}$Since the mediator is bound within the film, the diffusion at thefilm/bulk interface is governed by the zero flux boundary condition.

$\begin{matrix}{{\frac{\partial m}{\partial\chi}}_{\chi = 1} = 0} & (50)\end{matrix}$

The observed flux (j_(obs)) of [M₂] to the electrode, where it isconverted to [M₁], can be measured at the electrode as current (I). Theflux can also be modeled as mediator diffusion to the electrode, asexpressed by Eq. (51).

$\begin{matrix}{j_{abs} = {\frac{I}{nFA} = {- {D_{A}\left( \frac{\mathbb{d}\left\lbrack M_{1} \right\rbrack}{\mathbb{d}x} \right)}_{x = 0}}}} & (51)\end{matrix}$Since the mediator cannot escape from the film (dm/dχ=0 at χ=1) the rateof [S] reacting within the film is proportional to the flux of reducedmediator at the electrode's surface. Thus, the rate of [S] converted to[P] within the bioelectronic interface can be calculated from I.

The substrate and product participate in a reversible, equilibrium withan enzyme-substrate complex. A modified Michaelis-Menten kinetic modelis most frequently used to describe the reversible behavior of theenzyme [Eq. (52)] (Segel, 1993).

$\begin{matrix}{{v_{p} = \frac{V_{\max}\left( {s - \frac{p}{K_{eq}}} \right)}{{s\left( {1 + \frac{p}{K_{ii}}} \right)} + {K_{ma}\left( {1 + \frac{p}{K_{is}}} \right)}}}{where}} & (52) \\{V_{\max} = \frac{\kappa^{2}\alpha\; m\;\omega}{\omega + m}} & (53) \\{K_{eq} = \frac{\omega\;\mu\; m}{{\rho\lambda}\;{K\left( {1 - m} \right)}}} & (54) \\{K_{ii} = \frac{\omega + m}{\lambda\left( {\rho + \omega} \right)}} & (55) \\{{K_{ma} = \frac{m + {K\left( {1 - m} \right)}}{\mu\left( {\omega + m} \right)}}{and}} & (56) \\{K_{is} = \frac{m + {K\left( {1 - m} \right)}}{{\lambda\;{K\left( {1 - m} \right)}} + {\lambda\rho}}} & (57)\end{matrix}$K_(ii) and K_(is) are the inhibition constants which represent theeffects of [P]_(∞) on the slope and the intercept of the 1/v-axis,respectively of the 1/v versus 1/s plot. The values can be calculatedfrom the values of K_(m) and V_(max); however, a more accuratedetermination can be made if a series of reciprocal plots areconstructed for a wide range of product concentrations. The slope andthe 1/I-axis intercept of each can be replotted versus the correspondingproduct concentration. K_(iip) and K_(mp) can be determined from thereplots of the 1/I-axis intercept and slope vs λ, respectively [Eqs.(58) and (59), respectively].

$\begin{matrix}{\frac{1}{V_{\max,{app}}} = {{\frac{1}{V_{mad}K_{iip}}\lbrack P\rbrack} + \frac{1}{V_{\max}}}} & (58) \\{{slope}_{1/{\lbrack S\rbrack}} = {{\frac{K_{ma}}{V_{\max}K_{mp}}\lbrack P\rbrack} + \frac{K_{ma}}{V_{\max}}}} & (59)\end{matrix}$Where V_(max,app) and V_(max) are the y-intercept at a given λ and they-intercept when λ=0, respectively.

The observable Thiele modulus (Φ_(i)), which is the ratio of intrinsicchemical reaction rate in the absence mass transfer limitations to therate of diffusion through the film, can be estimated using Eq. (60):

$\begin{matrix}{\Phi_{i} = \frac{v_{i}l^{2}}{D_{i}K_{i}C_{i}}} & (60)\end{matrix}$where D_(i) is the diffusion coefficient of component i into the filmand C_(i) the concentration of species i at the liquid-film interface.

In catalytic reactors, the effectiveness factor (η) is defined as themeasured reaction rate divided by the motion rate that would haveresulted if there were no diffusional resistance within the film. Thislatter is obtained by evaluating the reaction rate assuming theconcentration throughout the film is equal to that at the film/bulkboundary (χ=1):

$\begin{matrix}{\eta = \frac{\int_{\chi = 0}^{\chi = 1}{v_{P}\ d\;\chi}}{{{\int_{\chi = 0}^{\chi = 1}v_{P}}\ }_{\chi = 1}d\;\chi}} & (61)\end{matrix}$When η is close to 1, the reaction is relatively uninfluenced bydiffusion. However, when η is much less than 1, the observed reactionrate is controlled by diffusion within the film.

This mathematical model can be compared to the one previously developedby Bartlett and Pratt (Bartlett and Pratt, 1995) by assumingirreversible enzyme kinetics and irreversible mediator kinetics(k_(B)=0). Under these conditions, Eqs. (41) and (42) reduce to Eqs.(62) and (63), respectively:

$\begin{matrix}{\frac{\partial^{2}m}{\partial\chi^{2}} = {\frac{{sm}\;\kappa_{*}^{2}}{{m\;{\gamma_{*}\left( {{s\;\mu} + 1} \right)}} + s}\mspace{14mu}{and}}} & (62) \\{\frac{\partial^{2}s}{\partial\chi^{2}} = {\frac{{sm}\;\kappa_{*}^{2}\eta_{*}^{- 1}\gamma_{*}}{{m\;{\gamma_{*}\left( {{s\;\mu} + 1} \right)}} + s}\mspace{14mu}{where}}} & (63) \\{\kappa_{*}^{2} = \frac{{k_{A}\left\lbrack E_{T} \right\rbrack}l^{2}}{D_{A}}} & (64) \\{\eta_{*} = {\frac{D_{S}{k_{a}\left( {k_{- 2} + k_{3}} \right)}}{D_{A}k_{3}k_{2}}\mspace{14mu}{and}}} & (65) \\{\gamma_{*} = \frac{\left\lbrack M_{T} \right\rbrack{k_{a}\left( {k_{- 2} + k_{3}} \right)}}{k_{2}k_{3}{K_{S}\lbrack S\rbrack}_{\infty}}} & (66)\end{matrix}$Eq. (66) matches the comparable equation developed by Bartlett and Pratt(Bartlett and Pratt, 1995), suggesting that the irreversible model is aspecial case of the more general, reversible model developed here.

The initial reaction rate dependence on product concentration wasderived using the presented mathematical model (FIG. 11A). Forreversible enzymes, the product inhibits the enzyme's activity towardsthe substrate in a manner that resembles enzyme inhibition. To determinethe type of inhibition and values of the kinetic constants, the datawere plotted in Lineweaver-Burk form (FIG. 11B). FIG. 11B shows thedouble-reciprocal plot for multiple dimensionless productconcentrations. As λ increases, the slope and 1/I-intercepts of thedouble reciprocal plots increase, pivoting clockwise about a point ofintersection that does not lie on either axis. This trend ischaracterized by a mixed inhibition mechanism. The inhibition constants(Table 2) were estimated from the data presented in FIGS. 11A and 11B.

There are three major regions of the polarization curve of interest: (1)the oxidation current, (2) reduction current, and (3) the transitionbetween the oxidation and the reduction current. These regions of thepolarization curve are affected by K, μ, λ, κ, ω, η, α, and β.

FIGS. 12A and 12B show the effects of substrate concentration (throughμ) and product concentration (through λ) on the oxidation current,reduction current, and the apparent oxidation potential of theenzyme/mediator-modified electrode when X=1, Y=1, K=1, λ=1.0, κ=4.6081,ω=0.0015, ρ=0.0015, α−1, and β=1. For μ values less than 0.1, theoxidation current increases proportionately to μ, suggesting that theoxidation current is limited by substrate. As μ exceeds 0.1, theoxidation current begins to saturate, reaching a plateau as μ approaches3. On the other hand, increasing μ decreases the reduction current,consistent with the idea that μ inhibits the reverse (reduction)reaction. The half-wave potential shifts to more negative potentials(FIG. 12A with increasing μ.

FIG. 12B shows the effect of product concentration (through λ) on thepolarization curves. For λ values less than 0.1, the reduction currentincreases proportionately to λ, suggesting that the reduction current islimited by product. As λ exceeds 0.1, the reduction current begins tosaturate, reaching a plateau as λ approaches 3. The increase in thereduction current is accompanied with a decrease in the oxidationcurrent. The half-wave potential shifted to more positive potentialswith increasing λ [FIG. 3B].

To further explore the effects of μ and λ on the polarization curves,multiple reaction conditions [X=1, Y=1, K=1.714, κ=2.0608, ω=0.0162,ρ=0.0032, α=0.5714, and β=0.2857) and (X=1, Y=1, K=6.7742, κ=6.6246,ω=0.0029, ρ=0.0088, α=3.0, and β=4.0)] were also examined. For all ofthese parameter sets, similar trends were observed. Oxidation currentincreased proportionately with μ for μ values less than 0.1 and thensaturated as μ values approached 3. Reduction current increasedproportionately with λ for λ values less than 0.1 and then saturated asλ values approached 3. These results suggest that μ and λ stronglyinfluence the system's performance over a wide range of parameter space.

FIG. 13A shows the plot of η vs. Φ_(S) when X=1, Y=1, K=1, λ=1.0,κ=4.6081, ω=0.0015, ρ=0.0015 with varying values of μ. When Φ_(S)<0.1 ηapproaches unity, suggesting the bioelectronic interface is kineticallylimited. Upon increasing Φ_(S)>1, η decreases rapidly suggesting thatthe system becomes substrate diffusion limited. To fully understand theeffects of substrate diffusion, multiple reaction conditions [(X=1, Y=1,K=1.714, κ=2.0608, ω=0.0162, and ρ=0.0032) and (X=1, Y=1, K=6.7742,κ=6.6246, ω=0.0029, and ρ=0.0088] were studied (data not shown). For lowvalues of Φ_(S) (Φ_(S)<0.1) η approaches unity; however, when Φ_(S)increases (Φ_(S)>1) η decreases rapidly. Similarities between η vs.Φ_(S) plots for the different reaction systems suggest that a singlecurve can represent the behavior of the bioelectronic interface athighly oxidizing potentials for a range of concentrations and reactionconditions suitable of biocatalytic experiments.

FIG. 13B shows the effect of multiple values of λ on the plot η vs.Φ_(P) at various reaction conditions at an applied potential of −250 mVwhen X=1, Y=1, K=1, μ=1.0, κ=4.6081, ω=0.0015, and ρ=0.0015 at variousvalues of λ. The bioelectronic interface transitions from a kineticlimited regime to a diffusion limited regime as Φ_(P) approaches 0.1.Plots of η vs. Φ_(P) for multiple λ under multiple reaction conditions[(X=1, Y=1, K=1.714, κ=2.0608, ω=0.0162, and ρ=0.0032) and (X=1, Y=1,K=6.7742, κ=6.6246, ω=0.0029, and ρ=0.0088)] (data not shown),transition from the kinetic limited regime when Φ_(P)=0.1. The plots ofη vs. Φ_(P) suggest that a single curve can represent the behavior ofthe bioelectronic interface for a range of concentrations and reactionconditions suitable of biocatalytic experiments.

FIG. 14 shows the effects of D_(M) on the plot of η vs. Φ_(M) at anapplied potential of 250 mV when X=1, Y=1, K−1, μ=1.0, λ=1.0, ω=0.0015,and ρ=0.0015 at various values of m (FIG. 14). For Φ_(M)<0.1 ηapproaches unity suggesting that the bioelectronic interface iskinetically limited; however, for Φ_(M)>1 η decreases rapidly suggestingthat the system transitions form a kinetic limited regime to a diffusionlimited regime. The similarity between the plots of η vs. Φ_(M) suggeststhat the bioelectronic interface transitions from the kinetic limited tothe diffusion limited regime are independent of m. Other reactionconditions [(X=1, Y−1, K=1.714, μ=1.0, κ=2.0608, ω=0.0162, and ρ=0.0032)and (X=1, Y=1, K=6.7742, κ=6.6246, ω=0.0029, and ρ=0.0088)] wereexamined. When Φ_(M)>0.1 η approaches unity; however, η decreasesrapidly when Φ_(M) is increased. The plots of η vs. Φ_(M) are consistentwith the interface when X=1, Y=1, K=1, μ=1.0, λ=1.0, ω=0.0015, andρ=0.0015 suggesting a single curve can represent the behavior of thebioelectronic interface for a range of concentrations suitable ofbiocatalytic experiments.

FIGS. 15A and 15B show the effects of ω and ρ on the polarization curve.For the system where X=1, Y=1, K=1, μ=1, λ=1.0, κ=4.6081, ρ=0.0015, α=1,and β=1 the oxidation current increased proportionately to of ω(ω≤0.015) [FIG. 6A], suggesting that ω limits the oxidation current.Increasing ω (ω≥0.015), the increase in current is no longerproportional to ω, suggesting that ω no longer limits the oxidationcurrent; however, the reduction current decreases suggesting that thereduction current is limited by high values of ω. Upon increasing ω thehalf-wave potential becomes more negative.

FIG. 15B shows the effects of polarization curves (X=1, Y=1, K=1, μ=1,λ=1.0, κ=4.6081, ω=0.0015, α=1, and β=1) of different values of ρ. Thereduction current increases proportionately with ρ (ρ≤0.015); however,increasing ρ (ρ>0.015) the current increase is no longer proportional toρ, suggesting that the reduction current is no longer limited by ρ.Continuing to increase ρ (ρ>0.015) the oxidation current starts todecrease, decreasing the half-wave potential. The effects on theoxidation current, reduction current, and the half-wave potentialsuggest that ρ and ω have equal but opposite effects on thebioelectronic interface.

To understand the effects of ωand ρ on the polarization curves multiplereaction conditions [(X=1.0, Y=1.0, K=1.7143, μ=1.0 λ=1.0, κ=2.0608,α=0.5714, and β=0.2857) and (X=1, Y=1.0, K=6.7742, μ=1, λ=1.0, κ=6.6246,α=3.0, and β=4.0)] were also examined. For the system where X=1.0,Y=1.0, K=1.7143, μ=1.0, λ=1.0, κ=1.0608, α=0.5714, and β=0.2857 theoxidation and reduction current increased proportionately to of ω and ρ(ω≤0.015 and ρ≤0.0015), when increasing ω and ρ (ω≥0.015 and ρ≥0.015),the increase in current is no longer proportional to ω and ρ. Thehalf-wave potential for the interface remains constant. For the systemwhere X=1, Y=1.0, K=6.7742, μ=1, λ=1.0, κ=6.6246, α=3.0, and β=4.0 theoxidation and reduction current increased proportionately to of ω and ρ(ω≤0.015 and ρ≤0.0015), when increasing ω and ρ (ω≥0.015 and ρ≥0.015),the increase in current is no longer proportional to ω and ρ. Thehalf-wave potential for the interface remains constant. The oxidationcurrent, reduction current, and half-wave potential suggests that theeffects of ω and ρ are consistent independent of the reactionconditions.

FIG. 16, shows the effect of mediator kinetics (K) on the oxidationcurrent, reduction current and the apparent oxidation potential of theenzyme/mediator-modified electrode. The oxidation and reduction currentremain stable when changing K between 0.1 and 100. The oxidation andreduction currents began to decrease upon increasing K above 100 ordecreasing below 0.1, respectively, suggesting that the mediatorkinetics become limiting in these regimes.

The half-wave potential was found to be a function of K, and is given byEq. (67):

$\begin{matrix}{{\Delta\; E} = {\left( \frac{RT}{n\; F} \right){\ln(K)}}} & (67)\end{matrix}$where ΔE is the E_(1/2). Eq. (67) is no longer valid when K becomeslimiting.

A unified model for a bioelectronic interface in which an electronmediator and reversible enzyme are entrapped in a uniform film at theelectrode surface has been presented. The model can predict performanceof the bioelectronic interface for a given set of parameters (enzymekinetics, mediator kinetics, substrate/product diffusion, mediatordiffusion, substrate/product concentration, mediator concentration andelectrode potential), which can be determined experimentally. Thispredictive capability provides a mechanism to rationally design andoptimize bioelectronic interfaces for applications in biosensors,biocatalytic reactors, and biological fuel cells.

The above description is considered that of the preferred embodimentsonly. Modifications of the invention will occur to those skilled in theart and to those who make or use the invention. Therefore, it isunderstood that the embodiments shown in the drawings and describedabove are merely for illustrative purposes and not intended to limit thescope of the invention, which is defined by the following claims asinterpreted according to the principles of patent law, including thedoctrine of equivalent.

The invention claimed is:
 1. A bioelectronic device comprising: anelectrically conductive carbon electrode; and a bioelectronic interfacebonded to a surface of the electrically conductive carbon electrode, andconfigured to regenerate, the bioelectronic interface including acatalytically active material that facilitates electron transfer, thecatalytically active material configured to be releasably andelectrostatically bound directly or indirectly to the surface via apolyelectrolyte, wherein the polyelectrolyte is configured to beremovably and electrostatically bound to a non-thiol ionic linker thatis covalently bound to a carbon atom at the surface.
 2. The device ofclaim 1, wherein the catalytically active material includes an enzymethat is bound directly or indirectly to the polyelectroly.
 3. The deviceof claim 2, wherein the enzyme is an oxidoreductase, a dehydrogenase, asecondary alcohol dehydrogenase or a mannitol dehydrogenase.
 4. Thedevice of claim 1, wherein the non-thiol ionic linker is glycine.
 5. Thedevice of claim 1, wherein said polyelectrolyte is comprised of acompound that includes a linking moiety covalently bound to the carbonatom at the surface of the electrically conductive carbon electrode, andfurther includes at least one ionized moiety for achieving the direct orindirect electrostatic bonding of the catalytically active material tothe electrically conductive carbon electrode.
 6. The device of claim 1wherein the electrically conductive carbon electrode further includes acarbon substrate.
 7. The device of claim 6, wherein the carbon substrateis a vitreous carbon substrate.
 8. The device of claim 7, wherein thevitreous carbon substrate is a reticulated vitreous carbon electrode. 9.The device of claim 1, wherein the bioelectronic interface furthercomprises a redox cofactor that facilitates or enhances activity of thecatalytically active material.
 10. The device of claim 9, wherein thebioelectronic interface includes an electron mediator that reduces theelectrical potential needed to transfer electrons during a chemicalreaction.
 11. The device of claim 10, wherein the electron mediator istoluidine blue O, neutral red or Nile blue A.
 12. The device of claim 9,wherein the redox cofactor is covalently bound to a polyelectrolyte thatis electrostatically bound directly or indirectly to the surface of theelectrically conductive carbon electrode.
 13. The device of claim 9,wherein the redox cofactor is selected from nicotinamide adeninedinucleotide (NAD), nicotinamide adenine dinucleotide phosphate (NADP),flavin adenine dinucleotide (FAD), flavin mononucleotide (FMN), andcombinations thereof.
 14. The device of claim 12, wherein a boronatelinkage is used to bind the redox cofactor to said polyelectrolyte. 15.The device of claim 1, wherein the polyelectrolyte is polyethyleneimine.16. The device of claim 1, wherein the catalytically active material isassociated with polyelectrolyte multilayers (PEMs) that are boundtogether by alternating layers of oppositely charged polyelectrolytes.17. The device of claim 16, wherein a redox cofactor is associated withPEMs that are bound together by alternating layers of oppositely chargedpolyelectrolytes.
 18. The device of claim 16, wherein a redox cofactorand an electron mediator are associated with PEMs that are boundtogether by alternating layers of oppositely charged polyelectrolytes.19. The device of claim 16, wherein the oppositely chargedpolyelectrolytes are polyethyleneimine (PEl) and polyacrylic acid (PAA).20. The device of claim 1, wherein the polyelectrolyte ionically bonds adehydrogenase enzyme and a redox cofactor to an ionicallyfunctionalized, electrically conductive carbon electrode to which anelectron mediator is bound.
 21. The device of claim 20, wherein thecatalytically active material includes at least two differentcatalytically active components.
 22. The device of claim 21, whereinsaid catalytically active components comprise different enzymes thatcatalyze different reactions.
 23. The device of claim 22 wherein saidenzymes comprise a xylose isomerase and a mannitol dehydrogenase. 24.The device of claim 22, wherein a branched linking moiety and thepolyelectrolyte are used to couple the enzymes, and optionally couple aredox cofactor for one or both of the enzymes, and/or optionally couplean electron mediator for one or both of the redox cofactors.
 25. Thedevice of claim 1, wherein the covalent bond with a carbon atom is acarbon-nitrogen bond.
 26. The device of claim 1 containing no thiollinkages.
 27. The device of claim 1 wherein said interface ismolecularly self-assembled.
 28. The device of claim 2, wherein thepolyelectrolyte provides enzymatic surface coverage up to about3.3×10⁻¹¹ moles/cm².
 29. The device of claim 16 wherein each of the PEMshas a thickness between about one and about five nanometers.
 30. Amethod comprising: producing a bioelectronic device comprising bonding abioelectronic interface to a surface of an electrically conductivecarbon electrode, wherein the bioelectronics interface is configured toregenerate, the bioelectronic interface including a catalytically activematerial that facilitates electron transfer, the catalytically activematerial configured to be releasably and electrostatically bounddirectly or indirectly to the surface via a polyelectrolyte, wherein thepolyelectrolyte is configured to be removably and electrostaticallybound to a non-thiol ionic linker that is covalently bound to a carbonatom at the surface.